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BEGIN:VEVENT
SUMMARY:Romain Aimino (University of Porto)
DTSTART:20201113T140000Z
DTEND:20201113T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/1
DESCRIPTION:Title: Large deviations estimates for dynamical systems with stretch
ed exponential decay of correlations\nby Romain Aimino (University of
Porto) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nDur
ing this talk\, I will discuss results on large deviations estimates for d
ynamical systems with stretched exponential decay of correlations. This cl
ass of systems encompasses for instance Viana maps and intermittent maps e
xhibiting a stretched exponential fast accumulation of pre-orbits at 0. Op
timal rates for large deviations of such systems are still unknown. I will
present a substancial improvement obtained in a joint work with Jorge Fre
itas.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeor Hafouta (Ohio State University)
DTSTART:20201120T140000Z
DTEND:20201120T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/2
DESCRIPTION:Title: Limit theorems for some time-dependent expanding dynamical sy
stems\nby Yeor Hafouta (Ohio State University) as part of Zoominar in
Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Matheus (Centre de Mathématiques Laurent Schwartz)
DTSTART:20201127T140000Z
DTEND:20201127T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/3
DESCRIPTION:Title: Speed of mixing of geodesic flows on certain non-positively c
urved surfaces\nby Carlos Matheus (Centre de Mathématiques Laurent Sc
hwartz) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nIn
this talk\, we discuss the speed of mixing on certain surfaces whose curv
atures are negative except along a closed geodesic. This is a joint work i
n progress with Y. Lima and I. Melbourne\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaqueline Siqueira (Universidade Federal do Rio de Janeiro)
DTSTART:20201204T140000Z
DTEND:20201204T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/4
DESCRIPTION:Title: Equilibrium states for a class of non-uniformly hyperbolic ma
ps\nby Jaqueline Siqueira (Universidade Federal do Rio de Janeiro) as
part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe consider a
wide family of non-uniformly hyperbolic maps and hyperbolic potentials an
d prove that the unique equilibrium state associated to each element of th
e family is given by the eigenmeasure and the eigenfunction of the transfe
r operator (both having the spectral radius as an eigenvalue). We prove th
at the transfer operator has the spectral gap property in the space of Ho
̈lder continuous observables. From this we derive that the unique equilib
rium state satisfies a central limit theorem and that it has exponential d
ecay of correlations. Moreover\, we prove joint continuity and analyticity
with respect to the potential. (Based on various joint works with S. Afon
so\, J. Alves\, V. Ramos.)\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20201218T140000Z
DTEND:20201218T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/6
DESCRIPTION:Title: Central limit theorems for counting measures in coarse negati
ve curvature\nby Giulio Tiozzo (University of Toronto) as part of Zoom
inar in Dynamical Systems @ Porto\n\n\nAbstract\nWe establish general cent
ral limit theorems for an action of a group on a hyperbolic space with res
pect to counting for the word length in the group. In 2013\, Chas\, Li\, a
nd Maskit produced numerical experiments on random closed geodesics on a h
yperbolic pair of pants. Namely\, they drew uniformly at random conjugacy
classes of a given word length\, and considered the hyperbolic length of t
he corresponding closed geodesic on the pair of pants. Their experiments
lead to the conjecture that the length of these closed geodesics satisfies
a central limit theorem\, and we proved this conjecture in 2018. In our n
ew work\, we remove the assumptions of properness and smoothness of the sp
ace\, or cocompactness of the action\, thus proving a general central limi
t theorem for group actions on hyperbolic spaces. We will see how our tech
niques replace the classical thermodynamic formalism and allow us to provi
de new applications\, including to lengths of geodesics in geometrically f
inite manifolds and to intersection numbers with submanifolds. Joint work
with I. Gekhtman and S. Taylor.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong-Kun Zhang (University of Massachusetts Amherst)
DTSTART:20210115T140000Z
DTEND:20210115T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/7
DESCRIPTION:Title: Levy diffusion for Lorentz gas with flat points\nby Hong-
Kun Zhang (University of Massachusetts Amherst) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nWe investigate the diffusion and st
atistical properties of Lorentz gas with cusps at flat points. The under
lying dynamical systems are modifications of dispersing billiards with
cusps. The systems generate stochastic processes with slow mixing rates
of order $n^{-a$}\, for $ a\\in (0\,1)$. We are able to show that these
stochastic processes enjoy stable law and have super-diffusion driven b
y Levy processes.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jairo Bochi (PUC Santiago de Chile)
DTSTART:20210122T140000Z
DTEND:20210122T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/8
DESCRIPTION:Title: Topological emergence\nby Jairo Bochi (PUC Santiago de Ch
ile) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nI wil
l explain the notion of topological emergence of a dynamical system\, intr
oduced by Pierre Berger and myself (2019). Topological emergence is a meas
urement of diversity of statistical behavior\, and it is independent of th
e traditional notions of dynamical complexity\, such as entropy. I will sh
ow an universal bound on topological emergence depending on the ambient di
mension\, and I will discuss the problem of computing topological emergenc
e of some hyperbolic dynamical systems. I will sketch the proofs.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Cristina Freitas (University of Porto)
DTSTART:20210129T140000Z
DTEND:20210129T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/9
DESCRIPTION:Title: The cluster size distribution and the extremal index\nby
Ana Cristina Freitas (University of Porto) as part of Zoominar in Dynamica
l Systems @ Porto\n\n\nAbstract\nThe extremal index appears as a parameter
in Extreme Value Laws for stochastic processes\, characterising the clust
ering of extreme events. We apply this idea in a dynamical systems context
to analyse the possible Extreme Value Laws for the stochastic process gen
erated by observations taken along dynamical orbits. In this context\, the
existence of an extremal index less than 1 is associated to the occurrenc
e of periodic phenomena. For generic points\, the exceedances\, in the lim
it\, are singular and occur at Poisson times. However\, around periodic po
ints\, the picture is different: the respective point processes of exceeda
nces converge to a compound Poisson process\, so instead of single exceeda
nces\, we have entire clusters of exceedances occurring at Poisson times w
ith a geometric distribution ruling its multiplicity. The extremal index u
sually coincides with the reciprocal of the mean of the limiting cluster s
ize distribution. Here\, we build dynamically generated stochastic process
es with an extremal index for which that equality does not hold. The mecha
nism we use is based on considering observable functions maximized at at l
east two points of the phase space\, where one of them is an indifferent p
eriodic point. For the second point at which the observable function is ma
ximized we consider either a periodic or a nonperiodic point. We explore t
wo such examples and\, for each of them\, we compute the extremal index an
d present the corresponding cluster size distribution.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugen Mihailescu (IRMAR)
DTSTART:20210205T140000Z
DTEND:20210205T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/10
DESCRIPTION:Title: Dynamics for a class of skew-product endomorphisms and appli
cations\nby Eugen Mihailescu (IRMAR) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nI will present a new notion of Smale endomo
rphisms and the skew-products coded by them. Equilibrium measures are stud
ied for these piecewise smooth transformations\; their projections are sho
wn to be exact dimensional in fibers and globally\, and dimension formulas
are obtained. This applies to skew-products over EMR maps and natural ext
ensions. Then we extend the Doeblin-Lenstra Conjecture on Diophantine appr
oximation coefficients for a larger class of measures and of irrational nu
mbers. Another application is to a type of complex continued fractions wit
h complex digits. Based on joint work with M. Urbanski.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Jurga (University of St Andrews)
DTSTART:20210212T140000Z
DTEND:20210212T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/11
DESCRIPTION:Title: Box dimensions of $(\\times m\, \\times n)$ invariant sets\nby Natalia Jurga (University of St Andrews) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nWe study the box dimensions of sets
which are invariant under the toral endormorphism $(x\, y) \\mapsto (m x \
\mod 1\, n y \\mod 1)$ for integers $n>m \\geq 2$. This is a fundamental
example of an expanding\, nonconformal dynamical system\, and invariant s
ets have many subtle properties. The basic examples of such invariant sets
are Bedford-McMullen carpets and\, more generally\, invariant sets are mo
delled by subshifts on the associated symbolic space. When this subshift i
s topologically mixing and sofic\, the situation is well-understood by res
ults of Kenyon and Peres\, in particular the box dimension satisfies a nat
ural formula in terms of entropy and the expansion coefficients $m\,n$. I
n this talk we will discuss what happens beyond the sofic and mixing case\
, which is partly based on joint work with Jonathan Fraser (St Andrews).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Kloeckner (Université Paris-Est)
DTSTART:20210219T140000Z
DTEND:20210219T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/12
DESCRIPTION:Title: Effective high-temperature estimates ensuring a spectral gap
\nby Benoît Kloeckner (Université Paris-Est) as part of Zoominar in
Dynamical Systems @ Porto\n\n\nAbstract\nThe main goal of the talk shall b
e to explain a few ideas from two classical theories : the thermodynamical
formalism\, and the perturbation of linear operators. The "thermodynamica
l formalism" is a framework to describe particular invariant measures of d
ynamical systems\, called "equilibrium states"\, parametrized by functions
on the phase space\, called "potentials". This formalism is based on the
"transfer operator"\; when this operator has a spectral gap\, the equilibr
ium state exists\, is unique\, and has very good statistical properties (e
xponential mixing\, Central Limit Theorem\, etc.) If one perturbs slightly
the potential\, the corresponding transfer operator is also perturbed. Th
e classical theory of perturbation of operators ensures that the spectral
gap property is an open condition and that under bounded pertubration\, th
e eigendata of an operator depends analytically on the perturbation. It tu
rns out that using the Implicit Function Theorem\, this theory can be made
effective with explicit bounds on the size of a neighborhood where the sp
ectral gap persists. Using this effective perturbation theory\, we show co
mpletely explicit bound on the potential ensuring the spectral gap propert
y for transfer operators of classical families of dynamical systems.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Rodriguez-Hertz (Pennsylvania State University)
DTSTART:20210226T140000Z
DTEND:20210226T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/13
DESCRIPTION:Title: Rigidity for expanding maps\nby Federico Rodriguez-Hertz
(Pennsylvania State University) as part of Zoominar in Dynamical Systems
@ Porto\n\n\nAbstract\nIn this talk I will discuss a plan started joint wi
th A. Gogolev to find rigidity property in hyperbolic dynamics. This plan
focuses on matching of smooth potentials for different dynamics. I will pr
esent a successful instance of this plan in the setting of expanding maps.
\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Shinoda (Keio University)
DTSTART:20210305T130000Z
DTEND:20210305T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/14
DESCRIPTION:Title: Non-convergence of equilibrium states at zero temperature li
mit\nby Mao Shinoda (Keio University) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe construct finite-range interactions on
a two dimensional symbolic dynamical system\, for which the associated equ
ilibrium states (i.e.\, the shift-invariant Gibbs states) fail to converge
as temperature goes to zero. More precisely\, if we pick any one-paramete
r family of equilibrium states at inverse temperature for this interaction
\, then the limit does not exist. This settles a question posed by Chazott
es and Hochman who obtained such a non-convergence behavior when dimension
greater than 3.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerôme Buzzi (Université de Paris-Saclay)
DTSTART:20210312T140000Z
DTEND:20210312T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/15
DESCRIPTION:Title: Continuity of Lyapunov exponents for surface diffeomorphisms
\nby Jerôme Buzzi (Université de Paris-Saclay) as part of Zoominar i
n Dynamical Systems @ Porto\n\n\nAbstract\nIn the setting of smooth surfac
e diffeomorphisms\, we show that the lower semicontinuity defect of the ex
ponents bounds that of the entropy. In particular\, Hausdorff dimension is
upper semicontinuous among ergodic invariant probability measures with en
tropy bounded away from zero. We also obtain a new criterion for the exist
ence of an SRB measure with positive entropy. Joint work with Sylvain CROV
ISIER and Omri SARIG.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Lima (Federal University of Ceará)
DTSTART:20210319T140000Z
DTEND:20210319T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/16
DESCRIPTION:Title: Symbolic dynamics for maps with high dimension\nby Yuri
Lima (Federal University of Ceará) as part of Zoominar in Dynamical Syste
ms @ Porto\n\n\nAbstract\nWe construct Markov partitions for non-invertibl
e and/or singular nonuniformy hyperbolic systems defined on higher dimens
ional Riemannian manifolds. The gen- erality of the setup covers classical
examples not treated so far\, such as geodesic flows in closed manifolds
\, multidimensional billiard maps\, and Viana maps\, as well as includes a
ll the recent results of the literature. We also provide a wealth of appli
cations. Joint work with Ermerson Araujo and Mauricio Poletti.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bálasz Bárány (Budapest University of Technology and Economics)
DTSTART:20210326T140000Z
DTEND:20210326T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/17
DESCRIPTION:Title: On the convergence rate of the chaos game\nby Bálasz B
árány (Budapest University of Technology and Economics) as part of Zoomi
nar in Dynamical Systems @ Porto\n\n\nAbstract\nIn the 1988 textbook "Frac
tals Everywhere" M. Barnsley introduced an algorithm for generating fracta
ls through a random procedure which he called the chaos game. In this talk
we show how long it takes the orbit of the chaos game to reach a certain
density inside the attractor of a strictly contracting iterated function s
ystem of which we only assume that its lower dimension is positive. We sho
w that the rate of growth of this cover time is determined by the Minkowsk
i dimension of the push-forward of the shift invariant measure with expone
ntial decay of correlations driving the chaos game. As an application\, fo
r Bedford-McMullen carpets we completely characterise the family of probab
ility vectors which minimise the Minkowski dimension of Bernoulli measures
. Interestingly\, these vectors have not appeared in any other aspect of B
edford-McMullen carpets before. This is a joint work with Natalia Jurga an
d István Kolossváry.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Carvalho (University of Porto)
DTSTART:20210409T130000Z
DTEND:20210409T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/18
DESCRIPTION:Title: Generalized entropy functions\, variational principles and e
quilibrium states\nby Maria Carvalho (University of Porto) as part of
Zoominar in Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Froyland (University of New South Wales)
DTSTART:20210416T090000Z
DTEND:20210416T100000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/19
DESCRIPTION:Title: Stability and approximation of statistical limit laws\nb
y Gary Froyland (University of New South Wales) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nThe unpredictability of chaotic nonl
inear dynamics leads naturally to statistical descriptions\, including pro
babilistic limit laws such as the central limit theorem and large deviatio
n principle. A key tool in the Nagaev-Guivarc'h spectral method for establ
ishing statistical limit theorems is a "twisted" transfer operator. We pro
ve stability of the variance in the central limit theorem and the rate fun
ction from a large deviation principle with respect to deterministic and s
tochastic perturbations of the dynamics and perturbations induced by numer
ical schemes. We then apply these results to piecewise expanding maps in o
ne and multiple dimensions. This theory can be extended to uniformly hyper
bolic maps and in this setting we develop two new Fourier-analytic methods
to provide the first rigorous estimates of the variance and rate function
for Anosov maps. This is joint work with Harry Crimmins.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaughn Climenhaga (University of Houston)
DTSTART:20210430T130000Z
DTEND:20210430T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/20
DESCRIPTION:Title: Counting closed geodesics on surfaces without conjugate poin
ts\nby Vaughn Climenhaga (University of Houston) as part of Zoominar i
n Dynamical Systems @ Porto\n\n\nAbstract\nFor negatively curved Riemannia
n manifolds\, Margulis gave an asymptotic formula for the number of closed
geodesics with length below a given threshold. I will describe joint work
with Gerhard Knieper and Khadim War in which we obtain the corresponding
result for surfaces without conjugate points by first proving uniqueness o
f the measure of maximal entropy and then following the approach of recent
work by Russell Ricks\, who established the asymptotic estimates in the s
etting of CAT(0) geodesic flows.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Oprocha (University of Science and Technology\, Krakow)
DTSTART:20210423T130000Z
DTEND:20210423T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/21
DESCRIPTION:Title: On the dynamics of Lorenz maps\nby Piotr Oprocha (Univer
sity of Science and Technology\, Krakow) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nIn this talk we will present several dynami
cal properties of expanding Lorenz maps\, which roughly speaking are incre
asing interval maps with one point of discontinuity. We will put special e
mphasis on piecewise linear case: x -> beta x + alpha (mod 1) Among othe
r\, we will consider such properties as transitivity\, mixing\, renormaliz
ations\, minimal cycles and proper invariant sets.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polina Vytnova (University of Warwick)
DTSTART:20210514T130000Z
DTEND:20210514T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/22
DESCRIPTION:Title: Computing Hausdorff dimension of Bernoulli convolutions\
nby Polina Vytnova (University of Warwick) as part of Zoominar in Dynamica
l Systems @ Porto\n\n\nAbstract\nIt is well known that for any 01/2 is very intricate and has been a subject of intensive re
search which dates back to Erdos. To date\, it is not known whether or not
the measure is singular or absolutely continuous for a given s. The probl
em of computing the Hausdorff dimension of the measure is also open in gen
eral\, though there have been several major advances in recent years. \n I
n the talk I will discuss a new approach to uniform lower bounds on Hausdo
rff dimension of Bernoulli convolution measures\, based on random dynamics
.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART:20210521T130000Z
DTEND:20210521T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/23
DESCRIPTION:Title: Thermodynamic formalism for coarse expanding dynamical syste
ms\nby Tushar Das (University of Wisconsin - La Crosse) as part of Zoo
minar in Dynamical Systems @ Porto\n\n\nAbstract\nWe report on a joint pro
ject (https://arxiv.org/abs/1908.08270 or https://doi.org/10.1007/s00220-0
21-04058-2) with Giulio Tiozzo\, Feliks Przytycki\, Mariusz Urbanski\, and
Anna Zdunik that develops the thermodynamic formalism for weakly coarse e
xpanding dynamical systems (finite branched covers of locally connected sp
aces that possess some expansion). There are no assumptions of finiteness
of the postcritical set\, conformality\, holomorphy\, or smoothness in thi
s setting. After encoding the dynamics via geometric code trees\, our stoc
hastic laws follow from those for the shift dynamics on the associated cod
e space. The area is in its nascency and there are plenty of open problems
and directions that await exploration.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Shmerkin (University of British Columbia)
DTSTART:20210528T150000Z
DTEND:20210528T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/24
DESCRIPTION:Title: Beyond Furstenberg's intersection conjecture\nby Pablo S
hmerkin (University of British Columbia) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nHillel Furstenberg conjectured in the 1960s
that the intersections of closed ×2 and ×3-invariant Cantor sets have
“small” Hausdorff dimension. This conjecture was proved independently
by Meng Wu and by myself\; recently\, Tim Austin found a simple proof. I w
ill present some generalizations of the intersection conjecture and other
related results.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Kryzhevich (Saint Petersburg State University)
DTSTART:20210507T130000Z
DTEND:20210507T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/25
DESCRIPTION:Title: Interval translation maps\, their invariant measures and the
ir properties\nby Sergey Kryzhevich (Saint Petersburg State University
) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe study
properties of the so-called interval translation maps (ITMs). Informally\
, we consider interval exchange maps with overlaps. A survey on the recent
developments in this area will be given with some author’s results bein
g mentioned. For example\, we prove that any ITM admits a Borel probabilit
y non-atomic invariant measure. We introduce the so-called maximal invaria
nt measure that is the measure supported on the largest possible set. It w
ill be demonstrated that any ITM\, endowed with this measure\, is isomorph
ic to an interval exchange map. This will imply various corollaries: th
e estimate on the maximal number of non-atomic ergodic invariant measures\
, minimality if the symbolic model\, unique ergodicity\, ‘closing lemma
’\, etc. Besides\, we discuss the problem of robustness of invariant mea
sures with respect to small perturbations of the parameters of the system.
Finally\, a real-life model of risk management will be considered. We de
monstrate that this model can be reduced to an ITM and study the propertie
s of the obtained map.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dalia Terhesiu (University of Leiden)
DTSTART:20210604T130000Z
DTEND:20210604T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/26
DESCRIPTION:Title: Lorentz gases with small scatterers\nby Dalia Terhesiu (
University of Leiden) as part of Zoominar in Dynamical Systems @ Porto\n\n
\nAbstract\nWe study Lorentz gases with scatterer size going to zero. In
work in progress with Balint and Bruin\, we obtain a precise understanding
of the allowed path of taking limits as the size of the scatterers goes t
o zero and time goes to infinity so that the Central Limit Law (with non-s
tandard normalization) persists. This type of joint law is in the gist of
Boltzmann–Grad limit. Further we obtain joint local limit theorems and m
ixing as the size of the scatterers goes to zero and time goes to infinity
.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Sadovskaya (Penn State University)
DTSTART:20210611T130000Z
DTEND:20210611T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/27
DESCRIPTION:Title: Diffeomorphism cocycles over partially hyperbolic systems\nby Victoria Sadovskaya (Penn State University) as part of Zoominar in D
ynamical Systems @ Porto\n\n\nAbstract\nWe consider cocycles over an acces
sible partially hyperbolic system with values in the group of diffeomorphi
sms of a compact manifold M. We will discuss the following results for thi
s setting: existence of a continuous invariant family of Riemannian metric
s on M for a bounded cocycle\, continuity of a measurable conjugacy betwee
n two cocycles\, and a sufficient condition for existence of a continuous
conjugacy.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vilton Pinheiro (Federal University of Bahia)
DTSTART:20210618T130000Z
DTEND:20210618T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/28
DESCRIPTION:Title: Ergodic formalism and topological attractors\nby Vilton
Pinheiro (Federal University of Bahia) as part of Zoominar in Dynamical Sy
stems @ Porto\n\n\nAbstract\nWe introduce the concept of Baire Ergodicity
and Ergodic Formalism. Using them to study topological and statistical att
ractors\, we give several applications for maps of the interval\, expandin
g and partially hyperbolic maps\, strongly dissipative dynamics and skew-p
roducts. In dynamical systems with abundance of historical behavior (and
this includes all systems with some hyperbolicity\, in particular\, Axiom
A systems)\, we cannot use an invariant probability to control the asympto
tic topological/statistical behavior of a generic orbit\, except when it b
elongs to the basin of a periodic orbit of attraction. However\, Baire's E
rgodicity and Ergodic Formalism can also be applied in this context\, cont
ributing to the study of generic orbits of systems with an abundance of hi
storical behavior.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davor Dragičević (University of Rijeka)
DTSTART:20210702T130000Z
DTEND:20210702T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/29
DESCRIPTION:Title: Quenched limit theorems for expanding on average cocycles\nby Davor Dragičević (University of Rijeka) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nIn [1\, 2]\, the authors extended th
e classical spectral method for establishing limit theorems for determinis
tic dynamical systems to random piecewise-expanding and hyperbolic dynamic
al systems exhibiting uniform decay of correlations. In this talk we will
discuss a certain modification of this method that enables us to establish
limit theorems for a class of random piecewise expanding dynamics that do
esn't exhibit uniform decay of correlations. This is a joint work with Jul
ien Sedro [3].\n \n[1] D. Dragičević et. al. A spectral approach for qu
enched limit theorems for random expanding dynamical systems\, Comm. Math.
Phys. 360 (2018)\, 1121--1187. \n[2] D. Dragičević et. al. A spectral a
pproach for quenched limit theorems for random hyperbolic dynamical system
s\, Trans. Amer. Math. Soc. 373 (2020)\, 629--664. \n[3] D. Dragičević a
nd J. Sedro\, Quenched limit theorems for expanding on average cocycles\,
preprint (2021)\, https://arxiv.org/abs/2105.00548\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafael Potrie (Universidad de la Republica)
DTSTART:20210709T130000Z
DTEND:20210709T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/30
DESCRIPTION:Title: Ergodicity of a class of partially hyperbolic systems\nb
y Rafael Potrie (Universidad de la Republica) as part of Zoominar in Dynam
ical Systems @ Porto\n\n\nAbstract\nWe study the problem of determining wh
en a partially hyperbolic diffeomorphism in dimension 3 is ergodic without
need for perturbations. We show that for a large class of such systems\,
that we called collapsed Anosov flows and which cover full connected compo
nents of partially hyperbolic systems we have ergodicity unless there is a
torus tangent to the $su$-direction which is known to impose strong condi
tions on the topology of the underlying manifold. I will try to explain th
e context of this result\, and hopefully be able to provide some taste of
the proofs. This is joint work with S. Fenley.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerôme Rousseau (Federal University of Bahia & University of Port
o)
DTSTART:20210709T140000Z
DTEND:20210709T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/31
DESCRIPTION:Title: Longest common substring for random subshifts of finite type
\nby Jerôme Rousseau (Federal University of Bahia & University of Por
to) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe stu
dy the behaviour of the longest common substring for random subshifts of f
inite type. We prove that\, under some exponential mixing assumptions\, th
is behaviour is linked to the Rényi entropy. We will show quenched and an
nealed results. In particular\, we will see that in the quenched case we o
btain a phase transition which does not appear in the annealed case. This
talk includes some joint works with Adriana Coutinho\, Rodrigo Lambert\, S
ébastien Gouezel and Manuel Stadlbauer.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Rivera-Letelier (University of Rochester)
DTSTART:20210709T150000Z
DTEND:20210709T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/32
DESCRIPTION:Title: Prime orbit counting for Collet-Eckmann maps\nby Juan Ri
vera-Letelier (University of Rochester) as part of Zoominar in Dynamical S
ystems @ Porto\n\n\nAbstract\nA discussion of prime orbit counting results
for real and complex maps\, where periodic orbits are weighted according
to their Lyapunov exponents. For real and complex maps satisfying the Coll
et-Eckmann condition\, we obtain a result with a power savings error term.
In comparison with the hyperbolic case\, the main technical difficulty st
ems from the relatively wild geometric properties of the absolutely contin
uous invariant measure. This is a joint work with Li Zhiqiang.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Crovisier (Université Paris-Saclay)
DTSTART:20210910T130000Z
DTEND:20210910T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/33
DESCRIPTION:Title: Strong positive recurrence for surface diffeomorphisms\n
by Sylvain Crovisier (Université Paris-Saclay) as part of Zoominar in Dyn
amical Systems @ Porto\n\n\nAbstract\nWe introduce the strong positive rec
urrence property for diffeomorphisms of a manifold and show that it holds
for every C-infinity surface diffeomorphism with positive topological entr
opy. It implies that the ergodic measures maximizing the entropy have expo
nential decay of correlations and satisfy a central limit theorem. This is
a joint work with J. Buzzi and O. Sarig.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Godofredo Iommi (PUC - Chile)
DTSTART:20210910T140000Z
DTEND:20210910T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/34
DESCRIPTION:Title: An ergodic theorem for symmetric averages\nby Godofredo
Iommi (PUC - Chile) as part of Zoominar in Dynamical Systems @ Porto\n\n\n
Abstract\nWe introduce a notion of barycenter of a probability measure rel
ated to the symmetric mean of a collection of nonnegative real numbers. Ou
r definition is inspired by the work of Halász and Székely\, who in 1976
proved a law of large numbers for symmetric means. We establish fundament
al inequalities that relate the symmetric mean of a list of nonnegative re
al numbers with the barycenter of the measure uniformly supported on these
points. As a consequence\, we go on to establish an ergodic theorem stati
ng that the symmetric means of a sequence of dynamical observations conver
ges to the Halász-Székely barycenter of the corresponding distribution.
This is joint work with Jairo Bochi and Mario Ponce.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenichiro Yamamoto (Nagaoka University)
DTSTART:20210924T130000Z
DTEND:20210924T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/35
DESCRIPTION:Title: Large deviation principle for piecewise monotonic maps with
density of periodic measures\nby Kenichiro Yamamoto (Nagaoka Universit
y) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nWe show
that a piecewise monotonic map with positive topological entropy satisfie
s the level-2 large deviation principle with a unique measure of maximal e
ntropy as reference under the conditions that the corresponding Markov dia
gram is irreducible and that the periodic measures of the map are dense in
the set of ergodic measures. This result can apply to a broad class of pi
ecewise monotonicmaps\, such as monotonic mod one transformations and piec
ewise monotonic maps with two monotonic pieces.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Darji (University of Louisville)
DTSTART:20210924T140000Z
DTEND:20210924T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/36
DESCRIPTION:Title: Generalized Hyperbolicity and the Shadowing Property in Line
ar Dynamics\nby Dario Darji (University of Louisville) as part of Zoom
inar in Dynamical Systems @ Porto\n\n\nAbstract\nIn this talk we discuss r
ecent results and open questions concerning in Hyperbolicity\, Generaliz
ed Hyperbolicity and the Shadowing Property in the setting of linear dynam
ics. In particular\, we discuss some results concerning when the Generaliz
ed Hyperbolicity is equivalent to the Shadowing Property. This talk will b
e accessible to grad students and non-specialists. All notions and backgro
und material will be clearly explained.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catalina Freijo (University of Lisbon)
DTSTART:20211008T130000Z
DTEND:20211008T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/37
DESCRIPTION:Title: Lyapunov exponents for non-uniformly fiber bunched linear co
cycles\nby Catalina Freijo (University of Lisbon) as part of Zoominar
in Dynamical Systems @ Porto\n\n\nAbstract\nWe consider a fixed hyperbolic
dynamics in the base and perturb the cocycle for studying the continuity
of Lyapunov exponents. For the case of uniformly fiber bunched cocycles\,
continuity was proved by Backes\, Brown and Butler. In this work we presen
t a characterization for continuity in the case of non-uniformly fiber bun
ched dynamics which is a partial answer to the conjecture of Marcelo Viana
. This is a joint work with Karina Marin (UFMG).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvius Klein (PUC-Rio de Janeiro)
DTSTART:20211008T140000Z
DTEND:20211008T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/38
DESCRIPTION:Title: Mixed random-quasiperiodic cocycles\nby Silvius Klein (P
UC-Rio de Janeiro) as part of Zoominar in Dynamical Systems @ Porto\n\n\nA
bstract\nThe purpose of this talk is to introduce the concept of mixed ran
dom-quasiperiodic linear cocycles and to discuss the ergodicity of its bas
e dynamics as well as the positivity and continuity of the corresponding
Lyapunov exponent. This is part of a larger joint project with Ao Cai and
Pedro Duarte (both from the University of Lisbon) whose aim is to study th
e stability under random perturbations of certain quasiperiodic systems.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Tahzibi (University of São Paulo - ICMC)
DTSTART:20211022T130000Z
DTEND:20211022T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/39
DESCRIPTION:Title: Equilibrium states for discretized Anosov flows\nby Ali
Tahzibi (University of São Paulo - ICMC) as part of Zoominar in Dynamical
Systems @ Porto\n\n\nAbstract\nWe consider partially hyperbolic diffeomor
phisms which appeared in the classification of partially hyperbolic diffeo
morphisms homotopic to identity on three-manifolds. In a previous result w
ith Buzzi and Fisher we constructed measures of maximal entropy for such d
iffeomorphisms and later proved some rigidity result about such measures j
oint with Buzzi-Crovisier-Poletti. In this talk we announce also some exis
tence/construction results and discuss uniqueness of (u-)equilibrium state
s in this setting in a work that is essentially part of the thesis of my
student Richard Becerra.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kucherenko (CCNY)
DTSTART:20211022T140000Z
DTEND:20211022T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/40
DESCRIPTION:Title: Flexibility of the Pressure Function\nby Tamara Kucheren
ko (CCNY) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\n
We discuss the flexibility of the pressure function of a continuous potent
ial (observable) with respect to a parameter regarded as the inverse tempe
rature. The points of non-differentiability of this function are of partic
ular interest in statistical physics\, since they correspond to phase tran
sitions. It is well known that the pressure function is convex\, Lipschitz
\, and has an asymptote at infinity. We prove that in a setting of one-dim
ensional compact symbolic systems these are the only restrictions. We pres
ent a method to explicitly construct a continuous potential whose pressure
function coincides with any prescribed convex Lipschitz asymptotically li
near function starting at a given positive value of the parameter. As a c
onsequence\, we obtain that for a continuous observable the phase transiti
ons can occur at a countable dense set of temperature values. We go furth
er and show that one can vary the cardinality of the set of ergodic equil
ibrium states as a function of the parameter to be any number\, finite or
infinite. This is based on joint work with Anthony Quas.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Lukina (University of Vienna)
DTSTART:20211105T140000Z
DTEND:20211105T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/41
DESCRIPTION:Title: Weyl groups and the growth of cycles in actions on rooted tr
ees\nby Olga Lukina (University of Vienna) as part of Zoominar in Dyna
mical Systems @ Porto\n\n\nAbstract\nMaximal tori and Weyl groups play an
important role in the study of compact connected Lie groups. In this talk\
, we introduce an analogous notion for profinite groups acting on rooted t
rees. We then use Weyl groups to study the conjecture by Boston and Jones\
, that settled elements are dense in the images of representations of abso
lute Galois groups of number fields into automorphism groups of rooted tre
es. An element is settled if it satisfies certain conditions on the growth
of cycles in its restrictions to finite levels of the tree. This is joint
work with Maria Isabel Cortez.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Carrasco (Federal University of Minas Gerais)
DTSTART:20211105T150000Z
DTEND:20211105T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/42
DESCRIPTION:Title: Non-uniformly hyperbolic endomorphisms\nby Pablo Carrasc
o (Federal University of Minas Gerais) as part of Zoominar in Dynamical Sy
stems @ Porto\n\n\nAbstract\nConsider an endomorphism E of the 2-dimension
al torus (a matrix with integer coefficients and determinant equal to one)
and suppose that it is not a multiple of the identity. Then there exists
an endomorphism homotopic to E that is area preserving and which is robust
ly (C1!) non-uniformly hyperbolic\; it has one positive and one negative L
yapunov exponent\, almost everywhere with respect to Lebesgue. This resul
t is part of a joint work with Martin Andersson (UFF) and Radu Saghin (PUC
V).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Panti (University of Udine)
DTSTART:20211119T140000Z
DTEND:20211119T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/43
DESCRIPTION:Title: Attractors of dual continued fractions\nby Giovanni Pant
i (University of Udine) as part of Zoominar in Dynamical Systems @ Porto\n
\n\nAbstract\nWe identify continued fractions with piecewise-projective Ma
rkov maps on some interval\, provided that all branches are induced by ele
ments in a fixed Hecke triangle group. Ordinary continued fractions consti
tute a very special case\, relative to the (2\,3\,infinity) group. The bra
nches of the map are expanding on the domain interval\, but contracting on
some other part of the real projective line. As such\, they give rise to
an IFS whose attractor is relevant\, since it determines the natural exten
sion and several properties\, both algebraic and dynamical\, of the origin
al system. We use an appropriate generalization of the classical Minkowski
Question Mark function to simultaneously linearize all maps resulting fro
m the same triangle group\, and to prove that the above IFS satisfies the
open set condition. We draw consequences -as well as open problems- from t
hese facts.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Sedro (LPSM-Paris)
DTSTART:20211203T140000Z
DTEND:20211203T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/44
DESCRIPTION:Title: Fractional susceptibility functions for the quadratic family
.\nby Julien Sedro (LPSM-Paris) as part of Zoominar in Dynamical Syste
ms @ Porto\n\n\nAbstract\nIn the last two decades\, a clear picture of lin
ear response for one-dimensional dynamics emerged. However\, in the specif
ic instance of the quadratic family\, two seemingly contradictory results
coexist: Ruelle proved in 2005 that the formal candidate for the derivativ
e of the response function at 0 was well defined\, through the study of th
e susceptibility function\, while Baladi et al. proved in 2014 that the sa
me response function was at best 1/2 Hölder at 0. To try to "shed some l
ight on this puzzling state of affairs"\, Baladi and Smania introduced so
called fractional susceptibility functions\, which are complex functions o
f two complex variables\, and relate to fractional response in the same wa
y the susceptibility function relates to linear response. I will present r
esults establishing holomorphy on a disk of radius larger than one for sim
plified fractional susceptibility functions\, as well as explain the strat
egy to extend this result to the 'true' fractional susceptibility function
.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Schapira (University of Rennes)
DTSTART:20211203T150000Z
DTEND:20211203T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/45
DESCRIPTION:by Barbara Schapira (University of Rennes) as part of Zoominar
in Dynamical Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Smania (University of São Paulo - ICMC)
DTSTART:20211119T150000Z
DTEND:20211119T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/46
DESCRIPTION:Title: Birkhoff sums as distributions\nby Daniel Smania (Univer
sity of São Paulo - ICMC) as part of Zoominar in Dynamical Systems @ Port
o\n\n\nAbstract\nUnder conditions (sufficiently fast decay of correlations
) that are satisfied in various settings we can consider Birkhoff sums as
distributions in the Schwartz sense (as in the study of PDEs) and study th
eir regularity. We will do this study in the case of piecewise expanding o
ne-dimensional maps and some other cases. This study makes intensive use o
f the statistical properties of the dynamic systems under consideration (d
ecay of correlations\, central limit theorem). In addition to its intrinsi
c interest\, this study is motivated by the theory of deformations of dyna
mical systems\, something similar to Teichmuller's theory for compact Riem
ann surfaces\, but in infinite dimension\, which has applications in impor
tant questions about the perturbation of dynamical systems\, such as the p
roblem of linear response. Indeed\, in one-dimensional dynamics topologica
l classes often have a differentiable structure\, that is\, they are infin
ite-dimensional Banach manifolds\, and the study of Birkhoff sums as distr
ibutions has a surprisingly important role here. Joint work with Clodoaldo
Ragazzo (IME-USP)\, but we will also cite several results with Viviane Ba
ladi and Amanda de Lima.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antti Käenmäki (University of Oulu)
DTSTART:20211217T140000Z
DTEND:20211217T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/47
DESCRIPTION:Title: Finer geometry of planar self-affine sets\nby Antti Käe
nmäki (University of Oulu) as part of Zoominar in Dynamical Systems @ Por
to\n\n\nAbstract\nFor a planar self-affine set satisfying the strong separ
ation condition\, it has been recently proved that under mild assumptions
the Hausdorff dimension equals the affinity dimension. In this article\, w
e continue this line of research\, and our objective is to acquire more re
fined geometric information in this setting. In a large class of such non-
carpet planar self-affine sets\, we characterize Ahlfors regularity\, dete
rmine the Assouad dimension of the set and its projections\, and estimate
the Hausdorff dimension of slices. We also demonstrate that the Assouad di
mension is not necessarily bounded above by the affinity dimension. The ta
lk is based on a recent work with Balázs Bárány and Han Yu.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Saussol (Université de Brest Occidentale)
DTSTART:20211217T150000Z
DTEND:20211217T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/48
DESCRIPTION:Title: Mikado of geodesics on negatively curved manifolds\nby B
enoit Saussol (Université de Brest Occidentale) as part of Zoominar in Dy
namical Systems @ Porto\n\n\nAbstract\nRecently Athreya\, Lalley\, Sapir a
nd Wroten have been interested in the tangle of geodesics in a compact rie
maniann surface of negative curvature. One question is to understand local
ly the picture of a geodesic segment of length T\, in a vicinity of any p
oint given on the surface. With Françoise Pène we recover their main res
ult\, applying our work on spatio-temporal point processes for visits to s
mall sets.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Lizana (Universidade Federal da Bahia)
DTSTART:20220121T140000Z
DTEND:20220121T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/49
DESCRIPTION:Title: Invariance of entropy for maps isotopic to Anosov\nby Cr
istina Lizana (Universidade Federal da Bahia) as part of Zoominar in Dynam
ical Systems @ Porto\n\n\nAbstract\nWe prove the topological entropy remai
ns constant inside the class of partially hyperbolic diffeomorphisms of T^
d with simple central bundle (that is\, when it decomposes into one dimens
ional sub-bundles with controlled geometry) and such that their induced ac
tion on H_1(T^d) is hyperbolic. In absence of the simplicity condition we
construct a robustly transitive counter-example. This is a joint work with
P. Carrasco\, E. Pujals and C. Vásquez.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Giulietti (Università di Pisa)
DTSTART:20220204T140000Z
DTEND:20220204T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/50
DESCRIPTION:Title: Quenched linear response for smooth expanding on average coc
ycles\nby Paolo Giulietti (Università di Pisa) as part of Zoominar in
Dynamical Systems @ Porto\n\n\nAbstract\nI will present an abstract quen
ched linear response result for random dynamical systems\, which applies t
o the case of smooth expanding on average cocycles on the unit circle. Con
fronting with the existing results in the literature\, the class of rando
m dynamics studied does not necessarily exhibit uniform decay of correlati
ons. Joint work with D. Dragicevic (Univ. of Rijeka) and J. Sedro (Sorbo
nne Univ.)\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Andersson (Universidade Federal Fluminense)
DTSTART:20220218T140000Z
DTEND:20220218T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/51
DESCRIPTION:Title: Non-uniformly expanding maps in the "wrong" homotopy classes
\nby Martin Andersson (Universidade Federal Fluminense) as part of Zoo
minar in Dynamical Systems @ Porto\n\n\nAbstract\nExamples of non-uniforml
y expanding maps are usually constructed by deforming a uniformly expandin
g map along a (locally supported) homotopy. In this talk I intend to expla
in how to create new examples of non-uniformly expanding maps by deforming
other kinds of maps\, including Anosov endomorphisms.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsutoshi Shinohara (Hitotsubashi University & Université de Bou
rgogne)
DTSTART:20220218T150000Z
DTEND:20220218T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/52
DESCRIPTION:Title: On A/D-converters and Fredholm determinants of piecewise lin
ear maps\nby Katsutoshi Shinohara (Hitotsubashi University & Universit
é de Bourgogne) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbs
tract\nBeta-encoders are A/D (Analog-to-Digital) encoders based on beta-ex
pansions. In order to give estimates of their quantization errors theoreti
cally\, the spectral analysis of Perron-Frobenius operators of correspondi
ng piecewise linear maps\, in other words\, the study of dynamical zeta fu
nctions\, plays an important role. I will give an introductory explanation
of this interplay between electronic circuit design theory and the theory
of one-dimensional dynamical systems. \nReference: Estimation of mean sq
uared errors of non-binary A/D-encoders through Fredholm determinants of p
iecewise-linear transformations https://doi.org/10.1587/nolta.9.243\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cagri Sert (University of Zurich)
DTSTART:20220128T150000Z
DTEND:20220128T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/53
DESCRIPTION:Title: Counting and boundary limit theorems for representations of
Gromov-hyperbolic groups\nby Cagri Sert (University of Zurich) as part
of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nLet $\\Gamma$ be
a hyperbolic group and S a finite symmetric generating set. The choice of
S determines a metric on $\\Gamma$ (namely the graph metric on the associa
ted Cayley graph). Given a representation $\\rho: \\Gamma \\to \\GL_d(\\R)
$\, we are interested in obtaining results analogous to random matrix prod
ucts theory (RMPT) but for the deterministic sequence of spherical average
s (with respect to S-metric). We will discuss a general law of large numbe
rs and more refined limit theorems such as central limit theorem and large
deviations. If time allows\, we will also see boundary limit theorems and
convergence of interpolated matrix norms along geodesic rays to the stand
ard Brownian motion. The techniques involve the existence of a coding for
hyperbolic groups\, RMPT in Markovian dependence and ergodicity of Patters
on--Sullivan measures. These as well as the connections with (and results
in) the classical RMPT will be discussed. Joint work with S. Cantrell.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Giordano Bruno (Università di Udine)
DTSTART:20220204T150000Z
DTEND:20220204T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/54
DESCRIPTION:Title: Topological and algebraic entropy on LCA groups\nby Anna
Giordano Bruno (Università di Udine) as part of Zoominar in Dynamical Sy
stems @ Porto\n\n\nAbstract\nSince its origin\, the algebraic entropy h_al
g was introduced in connection with the topological entropy h_top by means
of the Pontryagin - van Kampen duality. For a continuous endomorphism φ:
G → G of a locally compact abelian group G\, denote by \\hat G the Pont
ryagin dual group of G and by \\hat φ: G → G the dual endomorphism of
φ. In this talk\, we see under which assumptions the equality h_top(φ) =
h_alg(\\hat φ) is known to hold. We present the same connection also in
the much more general setting of (semi)group actions.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fagner B Rodrigues (Federal University of Rio Grande do Sul)
DTSTART:20220304T140000Z
DTEND:20220304T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/55
DESCRIPTION:Title: Properties of the set of entropy points of a free semigroup
action\nby Fagner B Rodrigues (Federal University of Rio Grande do Sul
) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nThe aim
of this talk is to present some local properties of the topological entrop
y of a free semigroup action. In order to do that we focus on the set of e
ntropy points of a free semigroup action\, show that this set carries the
full entropy of the system (which\, with respect to the chaocity of the sy
stem\, gives a fundamental relevance to such set). We prove that the topol
ogical entropy of a free semigroup action focuses on a countable set of po
ints. This is a joint work with Marcus V. Silva and Thomas Jacobus\, both
are PhD students of the PhD program of Mathematics and Statistics Institut
e of the Federal University of Rio Grande do Sul.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jamerson Bezerra (Copernicus University Torun)
DTSTART:20220304T150000Z
DTEND:20220304T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/56
DESCRIPTION:Title: Regularity of the Lyapunov exponent of random product of mat
rices\nby Jamerson Bezerra (Copernicus University Torun) as part of Zo
ominar in Dynamical Systems @ Porto\n\n\nAbstract\nIt is well established
in the literature that the Lyapunov exponent of the random product of matr
ices varies continuously with respect to the underlying data. However\, th
e understanding of the right modulus of continuity of this function remain
s an active problem with many contributions in the past years. In this tal
k we present an upper bound for the regularity of the Lyapunov exponent of
random product of (generic) matrices. This upper bound can be characteriz
ed in terms of metric properties of another essential invariant of the sys
tem namely the stationary measure.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Baker (University of Birmingham)
DTSTART:20220318T140000Z
DTEND:20220318T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/57
DESCRIPTION:Title: Normal numbers and self-similar measures\nby Simon Baker
(University of Birmingham) as part of Zoominar in Dynamical Systems @ Por
to\n\n\nAbstract\nA real number x is said to be normal in base b if the se
quence (b^n x) is uniformly distributed modulo one. In this talk I will di
scuss a recent result which states that for a self-similar measure and an
integer b\, if the self-similar measure and b satisfy a suitable arithmeti
c assumption\, then almost every x is normal in base b with respect to the
self-similar measure. This is a joint work with Amir Algom and Pablo Shme
rkin.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danijela Damjanovic (KTH)
DTSTART:20220318T150000Z
DTEND:20220318T160000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/58
DESCRIPTION:Title: Exploring the Borel-Smale example: centralizer rigidity for
maps and center rigidity for the action\nby Danijela Damjanovic (KTH)
as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nI will tal
k about our exploration of an interesting Z^2 Anosov action on a 2-step ni
lmanifold. Historically\, Anosov elements of this action were presented b
y Smale as first examples of Anosov maps which are not on the torus. We pr
ovide classification of centralizers for perturbations of certain non-Anos
ov elements of this action. We also show that the action itself is not loc
ally rigid\, but it still enjoys certain center-rigidity property under pe
rturbations. This is joint work with Amie Wilkinson and Disheng Xu.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoo Yokoyama (Gifu University)
DTSTART:20220408T130000Z
DTEND:20220408T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/59
DESCRIPTION:Title: Existence and Non-existence of Length Averages for Foliation
s\nby Tomoo Yokoyama (Gifu University) as part of Zoominar in Dynamica
l Systems @ Porto\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Spiewak (Bar-Ilan University)
DTSTART:20220422T130000Z
DTEND:20220422T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/60
DESCRIPTION:Title: Typical absolute continuity for classes of dynamically defin
ed measures\nby Adam Spiewak (Bar-Ilan University) as part of Zoominar
in Dynamical Systems @ Porto\n\n\nAbstract\nConsider a one-parameter fami
ly of iterated function systems on the interval and a family of measures o
n the corresponding symbolic space\, depending on the same parameter. We s
tudy geometric properties of measures projected by the natural projection
corresponding to the IFS. Assuming that IFS satisfies a transversality co
ndition and measures depend on the parameter regularly enough\, we obtain
results on the value of the dimension and absolute continuity of the proje
cted measure for almost every parameter. This extends classical results (f
or projections of a fixed measure) and applies e.g. to invariant measures
for systems with place-dependent probabilities and equilibrium measures fo
r hyperbolic iterated function systems. The talk is based on a recent join
t work with Balázs Bárány\, Károly Simon and Boris Solomyak.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastien Alvarez (Universidad de la Republica)
DTSTART:20220408T140000Z
DTEND:20220408T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/61
DESCRIPTION:Title: Metric entropy of foliations\nby Sebastien Alvarez (Univ
ersidad de la Republica) as part of Zoominar in Dynamical Systems @ Porto\
n\n\nAbstract\nThe topological dynamiucs of foliations is wll understood.
There is an analogue of periodic orbits\, limit sets\, recurrence\, and ev
en topological entropy\, following the work of Ghys\, Langevin and Walczak
. This entropy measures the transverse separation of the leaves of a folia
tion. This is not the case of the ergodic theory of foliations. In particu
lar\, there is no satisfactory version of metric entropy for foliations\,
and it is difficult to imagine a way to detect the separation of leaves us
ing measure theory (whether harmonic\, or invariant by certain dynamics ta
ngent to the leaves). For example is it possible to obtain a variational p
rinciple for foliations? In this talk\, I will discuss an approach made wi
th Jiagang Yang (UFF\, Niteroi) to attack this problem.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Zelerowicz (University of Maryland)
DTSTART:20220422T140000Z
DTEND:20220422T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/62
DESCRIPTION:Title: Lorentz gases on aperiodic tilings\nby Agnieszka Zelerow
icz (University of Maryland) as part of Zoominar in Dynamical Systems @ Po
rto\n\n\nAbstract\nIn this joint work with Rodrigo Treviño we consider t
he Lorentz gas model of category A (that is\, with no corners and of finit
e horizon) on aperiodic repetitive tilings of $\\mathbb{R}^2$ of finite lo
cal complexity. We show that the compact factor of the collision map has t
he K property\, from which we derive mixing for pattern-equivariant functi
ons as well as the planar ergodicity of the Lorentz gas flow.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Disheng Xu (Beijing University)
DTSTART:20220506T130000Z
DTEND:20220506T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/63
DESCRIPTION:Title: Some topics on compact center foliations of partially hyperb
olic systems\nby Disheng Xu (Beijing University) as part of Zoominar i
n Dynamical Systems @ Porto\n\n\nAbstract\nPartially hyperbolic systems is
a natural generalization of Anosov systems in dynamical systems. In this
talk we will focus on partially hyperbolic systems with invariant compact
center foliations\, and discuss some interesting properties and some recen
t results on the regularity of compact center foliations\, under different
conditions. This talk will be self-contained.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma D'Aniello (Universitá di Campania)
DTSTART:20220603T140000Z
DTEND:20220603T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/64
DESCRIPTION:Title: Some linear dynamics on Lp spaces\nby Emma D'Aniello (Un
iversitá di Campania) as part of Zoominar in Dynamical Systems @ Porto\n\
n\nAbstract\nWe investigate\, in the linear setting\, notions of chaos com
ing from topological dynamics\, and hyperbolic properties originally defin
ed in a non-linear framework. We focus in particular on “shift-like”
composition operators on arbitrary measure spaces\, a large class of linea
r operators that includes the weighted shifts as a special case.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luciana Salgado (Universidade Federal do Rio de Janeiro)
DTSTART:20220506T140000Z
DTEND:20220506T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/65
DESCRIPTION:Title: Ergodic and geometric aspects of singular flows\nby Luc
iana Salgado (Universidade Federal do Rio de Janeiro) as part of Zoominar
in Dynamical Systems @ Porto\n\n\nAbstract\nLyapunov functions provided by
quadratic forms are useful tools in Dynamical Systems. For instance\, th
ese are used in results of topological stability and ergodic properties as
found in works by Burns-Katok\, Lewowicz\, Markarian and Wojtkowski. Thi
s talk is about how to use the quadratic Lyapunov functions to show some e
rgodic and dynamical properties of singular flows (e.g. Lorenz flow).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Héctor Barge (Universidad Politécnica de Madrid)
DTSTART:20220520T140000Z
DTEND:20220520T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/66
DESCRIPTION:Title: Low-dimensional topology and the realization problem of attr
actors for non-connected compacta\nby Héctor Barge (Universidad Polit
écnica de Madrid) as part of Zoominar in Dynamical Systems @ Porto\n\n\nA
bstract\nIt is well known that if K = K_1 ⊔ . . . ⊔ K_r ⊂ R^n\, wher
e K_i is compact for each i\, is an attractor for a dynamical system (disc
rete or continuous) in R^n then K_i is an attractor for each i. In this ta
lk we shall study whether the converse statement holds:\n\n(S): If each K_
i is an attractor for a dynamical system so is K.\n\nWe shall see that (S)
holds true in the case of continuous dynamical systems. However\, the dis
crete case is more involved. In particular\, we will see that there exist
compacta in R^3 comprised of two connected components that can be realized
as attractors separately but whose union cannot be so realized. Finally\,
we will introduce a sufficient condition for (S) to hold true in the disc
rete case and we shall see that this condition is also sufficient in some
suitable situations. These results have been obtained in collaboration wit
h J.J. Sanchez-Gabites.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adriana Sanchez (CIMPA - Costa Rica)
DTSTART:20220603T130000Z
DTEND:20220603T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/67
DESCRIPTION:Title: Analiticity of the Lyapunov exponents of random products of
quasi-periodic cocycles\nby Adriana Sanchez (CIMPA - Costa Rica) as pa
rt of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nOne of the most
important questions that comes up when studying Lyapunov exponents of lin
ear cocycles is the regularity problem. By this we mean the problem of und
erstanding the behavior of the Lyapunov exponents regarding the underlying
data. It is a classical result of Peres [1] that\, for i.i.d. sequence of
matrices with discrete distribution\, the Lyapunov exponents are locally
analytic if mild simplicity conditions are assumed. In this talk we are go
ing to discuss an extension of Per ́es conclusions in [1] to include the
random product of quasi-periodic cocycles for the skew product base dynami
cs. This is a join work with Jamerson Bezerra and El Hadji Yaya Tall.\n\n[
1] Y. Peres. “Analytic dependence of Lyapunov exponents on transition pr
obabil- ities”. In: Lyapunov exponents (Oberwolfach\, 1990). Vol. 1486.
Lecture Notes in Math. Springer-Verlag\, 1991\, pp. 64–80.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Cerreia-Vioglio (Bocconi)
DTSTART:20220520T130000Z
DTEND:20220520T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/68
DESCRIPTION:Title: Ergodic Theorems for Lower Probabilities\nby Simone Cerr
eia-Vioglio (Bocconi) as part of Zoominar in Dynamical Systems @ Porto\n\n
\nAbstract\nWe establish an Ergodic Theorem for lower probabilities\, a ge
neralization of standard probabilities widely used in applications. As a b
y-product\, we provide a version for lower probabilities of the Strong Law
of Large Numbers (joint work with F. Maccheroni and M. Marinacci).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Freitas (University of Porto)
DTSTART:20220617T130000Z
DTEND:20220617T135000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/69
DESCRIPTION:Title: Point processes\, record events and heavy tails\nby Jorg
e Freitas (University of Porto) as part of Zoominar in Dynamical Systems @
Porto\n\n\nAbstract\nWe consider stochastic processes arising from chaoti
c systems and build multidimensional point processes which provide a nice
description regarding both the extremal behaviour\, the distribution of re
cord events and the convergence of functional limits for the sums of heavy
tailed observables.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minsung Kim (Copernicus University in Torún)
DTSTART:20220617T135000Z
DTEND:20220617T144000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/70
DESCRIPTION:Title: Deviation spectrum of Birkhoff integrals for locally Hamilt
onian flows on compact surfaces\nby Minsung Kim (Copernicus University
in Torún) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract
\nThis talk will consist of an introduction to the topic of deviation of B
irkhoff integrals for locally Hamiltonian flows on compact surfaces and re
cent related results. These works extend the study of the spectrum of devi
ations of ergodic integrals beyond the case where the observable vanishes
at the singularities. New developments include a better understanding of t
he asymptotics (in non-degenerate regime) and the appearance of new expone
nts in the deviation spectrum (in degenerate regime). This is joint work w
ith Krzysztof Frączek.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanja Schindler (University of Vienna)
DTSTART:20220617T145000Z
DTEND:20220617T154000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/71
DESCRIPTION:Title: A qualitative central limit theorem for certain unbounded ov
er piecewise expanding interval map\nby Tanja Schindler (University of
Vienna) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract\nM
any limit theorems in ergodic theory are proven using the spectral gap met
hod. So one of the main ingredients for this method is to have a space on
which the transfer operator has a spectral gap. However\, most of the clas
sical spaces\, like for example the space of Hölder or quasi-Hölder func
tion or BV functions don't allow unbounded functions. We will give such a
space which allows observables with a pole at the fixed points of a piecew
ise expanding interval transformation and state a quantitative central lim
it theorem using Edgeworth expansions. As an application we give a samplin
g result for the Riemann-zeta function over a Boolean type transformation.
This is joint work with Kasun Fernando.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sakshi Jain (Università degli Studi di Roma - Tor Vergata)
DTSTART:20220916T130000Z
DTEND:20220916T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/72
DESCRIPTION:Title: Discontinuities cause essential spectrum\nby Sakshi Jain
(Università degli Studi di Roma - Tor Vergata) as part of Zoominar in Dy
namical Systems @ Porto\n\n\nAbstract\nWe study transfer operators associa
ted to piecewise monotone interval transformations and show that the essen
tial spectrum is large for any relevant Banach space when the transformati
on fails to be Markov. Constructing a family of Banach spaces we show that
the lower bound on the essential spectral radius is optimal. Indeed\, the
se Banach spaces realise an essential spectral radius as close as desired
to the theoretical best possible case.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlene Kalle (University of Leiden)
DTSTART:20220930T130000Z
DTEND:20220930T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/73
DESCRIPTION:Title: Random intermittent dynamics\nby Charlene Kalle (Univers
ity of Leiden) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstr
act\nIntermittent dynamics\, where systems irregularly alternate between l
ong periods of different types of dynamical behaviour\, has been studied s
ince the work of Pomeau and Manneville in 1980. In random dynamical system
s this phenomenon has only been well understood in a few specific cases. A
random dynamical system consists of a family of deterministic systems\, o
ne of which is chosen to be applied at each time step according to some pr
obabilistic rule. In this talk we will describe the intermittency of some
families of random systems with a particular emphasis on how the intermitt
ency of the random system depends on the intermittency of the underlying d
eterministic systems. This talk is based on joint works with Ale Jan Hombu
rg\, Tom Kempton\, Valentin Matache\, Marks Ruziboev\, Masato Tsujii\, Evg
eny Verbitskiy and Benthen Zeegers.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Moreira (University of Warwick)
DTSTART:20221014T130000Z
DTEND:20221014T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/74
DESCRIPTION:Title: Infinite Ergodic Ramsey theory\nby Joel Moreira (Univers
ity of Warwick) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbst
ract\nIn the 1970's Furstenberg obtained an ergodic theoretic proof of Sze
meredi's theorem\, stating that any set of natural numbers with positive u
pper density contains arbitrarily long (but finite) arithmetic progression
s. Since then\, Furstenbeg's approach has been extended to many other comb
inatorial applications\, giving rise to the field of Ergodic Ramsey Theory
. However\, until recently\, ergodic theoretic methods were unable to hand
le infinite configurations. I will present recent joint work where we over
came this difficulty to answer some Ramsey theoretical questions raised by
Erdos in the 1980's using methods from ergodic theory.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ai-Hua Fan (Université de Picardie Jules Verne\, Amiens)
DTSTART:20221028T130000Z
DTEND:20221028T140000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/75
DESCRIPTION:Title: Some aspects of weighted Birkhoff averages: Bohr Chaoticity
and Multifractality\nby Ai-Hua Fan (Université de Picardie Jules Vern
e\, Amiens) as part of Zoominar in Dynamical Systems @ Porto\n\n\nAbstract
\nThe Sarnak conjecture\, which concerns with the Birkhoff averages weight
ed by the Möbius sequence in a topological dynamical system\, asserts tha
t all zero entropy systems are orthogonal to the Möbius sequence. Which s
ystems are orthogonal to none of non-trivial weighted? We qualify such sys
tems as Bohr chaotic. The Bohr chaoticity is a complexity measure and is a
topological invariant\; it implies the positivity of entropy. However\, t
he positivity of entropy doesn’t imply the Bohr chaoticity. We prove tha
t a system (X\, T) admitting a horseshoe (i.e a susbsytem of some power of
T is conjugate to a full shift) is Bohr chaotic. Thus usual nice systems
of positive entropy are Bohr chaotic. But systems having few ergodic measu
res are not Bohr chaotic. Another class of systems which are proved to be
Bohr chaotic are the algebraic principal systems. A second aspect of weigh
ted Birkhoff averages to be discussed will be its multifractal behaviors.
To this end\, a thermodynamical formalism is proposed\, but Gibbs measure
in this new setting are not ergodic with respect to the original dynamical
system. In the computation of the multifractal spectrum\, it arises a que
stion about a topological version of Furstenberg-Kesten theorem on product
s of non-negative matrices and a such version is obtained. Parts of result
s presented here are joint works with Shilei FAN (Wuhan)\, Valery RYZHYKOV
(Moscou)\, Klaus SCHMIDT (Vienne)\, Weixiao SHEN (Shanghai) et Evgeny VER
BITSIY (Leiden)\, Meng WU (Oulu)\; others are due to Matan TAL (Jerusalem)
\, Balazs BARANY (Budapest)\, Michal RAMS (Warsaw)\, Ruxi SHI (Paris).\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zemer Kosloff (Hebrew University of Jerusalem)
DTSTART:20221111T140000Z
DTEND:20221111T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/76
DESCRIPTION:Title: (Stationary) Bernoulli shift factors for inhomogeneous syste
ms\nby Zemer Kosloff (Hebrew University of Jerusalem) as part of Zoomi
nar in Dynamical Systems @ Porto\n\n\nAbstract\nJoint work with Terry Soo.
We will survey recent results on the model of nonsingular Bernoulli shift
s\, its relation to classical questions in smooth ergodic theory and discu
ss recent results on existence of (stationary) Bernoulli shift factors for
systems which are not measure preserving and the stark difference between
finitary and non-finitary factors.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ale Jan Homburg (KdV Institute for Mathematics - University of Ams
terdam)
DTSTART:20221209T140000Z
DTEND:20221209T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/77
DESCRIPTION:by Ale Jan Homburg (KdV Institute for Mathematics - University
of Amsterdam) as part of Zoominar in Dynamical Systems @ Porto\n\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magdalena Foryś-Krawiec (AGH - Krakow)
DTSTART:20221125T140000Z
DTEND:20221125T150000Z
DTSTAMP:20260404T111331Z
UID:Zoominar-CMUP/78
DESCRIPTION:Title: Irregular sets for maps with shadowing and their metric mean
dimension\nby Magdalena Foryś-Krawiec (AGH - Krakow) as part of Zoom
inar in Dynamical Systems @ Porto\n\n\nAbstract\nFor a dynamical system\,
a Φ-irregular set is the set of points x for which the Birkhoff averages
determined by Φ along the orbit of x diverge. Such sets\, however negligi
ble from ergodic theory point of view\, may have interesting dynamical pro
perties and complex structure. In the talk we present the characterization
of Φ-irregular sets in dynamical systems with shadowing over a chain rec
urrent class in terms of their metric mean dimension. The results presente
d in the talk are obtained as a joint work with Piotr Oprocha.\n
LOCATION:https://stable.researchseminars.org/talk/Zoominar-CMUP/78/
END:VEVENT
END:VCALENDAR