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BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto (Canada))
DTSTART:20200514T150000Z
DTEND:20200514T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/1
DESCRIPTION:Title: Central limit theorems for counting measures in coarse negative cu
rvature\nby Giulio Tiozzo (University of Toronto (Canada)) as part of
DinAmicI: Another Internet Seminar\n\n\nAbstract\nWe establish general cen
tral limit theorems for an action of a group on a hyperbolic space with re
spect to counting for the word length in the group.\nIn 2013\, Chas\, Li\,
and Maskit produced numerical experiments on random closed geodesics on a
hyperbolic pair of pants. Namely\, they drew uniformly at random conjuga
cy classes of a given word length\, and considered the hyperbolic length o
f the corresponding closed geodesic on the pair of pants. Their experi
ments lead to the conjecture that the length of these closed geodesics sat
isfies a central limit theorem\, and we proved this conjecture in 2018. \
nIn our new work\, we remove the assumptions of properness and smoothness
of the space\, or cocompactness of the action\, thus proving a general cen
tral limit theorem for group actions on hyperbolic spaces. \nWe will see
how our techniques replace the classical thermodynamic formalism and allow
us to provide new applications\, including to lengths of geodesics in geo
metrically finite manifolds and to intersection numbers with submanifolds.
\nJoint work with I. Gekhtman and S. Taylor.\n\nZoom link:\nhttps://unipd.
zoom.us/j/91001776009?pwd=Qm0wZVF3TWxmNm9LVFhYL0RiczBHdz09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Leguil (Université Paris-Sud 11 (France))
DTSTART:20200521T150000Z
DTEND:20200521T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/2
DESCRIPTION:Title: Some rigidity results for billiards and hyperbolic flows\nby M
artin Leguil (Université Paris-Sud 11 (France)) as part of DinAmicI: Anot
her Internet Seminar\n\n\nAbstract\nIn a project with P. Bálint\, J. De S
imoi and V. Kaloshin\, we have been studying the inverse problem for a cla
ss of open dispersing billiards obtained by removing from the plane a fini
te number of smooth strictly convex scatterers satisfying a non-eclipse co
ndition. The dynamics of such billiards is hyperbolic (Axiom A)\, and ther
e is a natural labeling of periodic orbits. We show that it is generically
possible\, in the analytic category and for billiard tables with two (par
tial) axial symmetries\, to determine completely the geometry of those bil
liards from the purely dynamical data encoded in their Marked Length Spect
rum (lengths of periodic orbits + marking). An important step is the obten
tion of asymptotic estimates for the Lyapunov exponents of certain periodi
c points accumulating a reference periodic point\, which turn out to be us
eful in the study of other rigidity problems. In particular\, I will expla
in the results obtained in a joint work with J. De Simoi\, K. Vinhage and
Y. Yang on the question of entropy rigidity for 3-dimensional Anosov flows
and dispersing billiards.\n\nZoom link: https://unipd.zoom.us/j/982208387
92?pwd=Njg2U1pnQXQ3Uno4Nit0RE13MzFnQT09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Cellarosi (Queen’s University (Canada))
DTSTART:20200528T150000Z
DTEND:20200528T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/3
DESCRIPTION:Title: Rational Horocycle lifts and the tails of Quadratic Weyl sums\
nby Francesco Cellarosi (Queen’s University (Canada)) as part of DinAmic
I: Another Internet Seminar\n\n\nAbstract\nEquidistribution of horocycles
on hyperbolic surfaces has been used to dynamically answer several probabi
listic questions about number-theoretical objects. In this talk we focus o
n horocycle lifts\, i.e. curves on higher-dimensional manifolds whose proj
ection to the hyperbolic surface is a classical horocycle\, and their beha
viour under the action of the geodesic flow. It is known that when such ho
rocycle lifts are `generic’\, then their push forward via the geodesic f
low becomes equidistributed in the ambient manifold. We consider certain
‘non-generic’ (i.e. rational) horocycle lifts\, in which case the equi
distribution takes place on a sub-manifold. We then use this fact to study
the tail distribution of quadratic Weyl sums when one of their arguments
is random and the other is rational. In this case we obtain random variabl
es with heavy tails\, all of which only possess moments of order less than
4. Depending on the rational argument\, we establish the exact tail decay
\, which can be described with the help of the Dedekind $\\psi$-function.\
n\nJoint work with Tariq Osman.\n\nZoom link: https://unipd.zoom.us/j/9162
5758001?pwd=NzU1SG5LZkxKVTI5SXBsSUpNUW5XQT09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Vaienti (Centre de Physique Théorique\, Marseille (France)
)
DTSTART:20200604T150000Z
DTEND:20200604T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/4
DESCRIPTION:Title: Thermodynamic formalism for random weighted covering systems\n
by Sandro Vaienti (Centre de Physique Théorique\, Marseille (France)) as
part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nWe develop a que
nched thermodynamic formalism for random dynamical systems generated by co
untably branched\, piecewise-monotone mappings of the interval that satisf
y a random covering condition.\n\nJoint with J. Atnip\, G. Froyland and C.
Gonzalez-Tokman\n\nZoom link: https://unipd.zoom.us/j/91644787447?pwd=UzZ
IbXg4Qms3NU9lek5Hd1dLZGR1Zz09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Maggioni (Leiden University)
DTSTART:20200701T150000Z
DTEND:20200701T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/5
DESCRIPTION:Title: Matching for random systems with an application to minimal weight
expansions\nby Marta Maggioni (Leiden University) as part of DinAmicI:
Another Internet Seminar\n\n\nAbstract\nWe consider families of skew-prod
uct maps\, representing systems evolving in discrete time in which\, at ea
ch time step\, one of a number of transformations is chosen according to a
n i.i.d process and applied. We extend the notion of matching for such dyn
amical systems and we show that\, for a certain family of piecewise affine
random maps of the interval\, the property of random matching implies tha
t any invariant density is piecewise constant. We give an application by i
ntroducing a one-parameter family of random maps generating signed binary
expansions of numbers. This family has random matching for Lebesgue almost
every parameter\, producing matching intervals that are related to the on
es obtained for the Nakada continued fraction transformations. We use this
property to study the expansions with minimal weight.\nJoint with K. Daja
ni\, and C. Kalle\n\nZoom link: https://unipd.zoom.us/j/98457166023?pwd=Q1
VSZUtEbk95QnVUYmVGVEpQMXk5UT09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunrose Shrestha (Tufts University\, USA)
DTSTART:20200617T150000Z
DTEND:20200617T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/7
DESCRIPTION:Title: The topology and geometry of random square-tiled surfaces\nby
Sunrose Shrestha (Tufts University\, USA) as part of DinAmicI: Another Int
ernet Seminar\n\n\nAbstract\nA square-tiled surface (STS) is a branched co
ver of the standard square torus with branching over exactly one point. Th
ey are concrete examples of translation surfaces which are an important cl
ass of singular flat metrics on 2-manifolds with applications in Teichmül
ler theory and polygonal billiards. In this talk we will consider a random
izing model for STSs based on permutation pairs and use it to compute the
genus distribution. We also study holonomy vectors (Euclidean displacement
vectors between cone points) on a random STS. Holonomy vectors of transla
tion surfaces provide coordinates on the space of translation surfaces and
their enumeration up to a fixed length has been studied by various author
s such as Eskin and Masur. In this talk\, we obtain finer information abou
t the set of holonomy vectors\, Hol(S)\, of a random STS. In particular\,
we will see how often Hol(S) contains the set of primitive integer vectors
and find how often these sets are exactly equal.\n\nZoom link: https://un
ipd.zoom.us/j/92074073847?pwd=ZDd6Y28yUVowcjJNUFFRYU52WGtTdz09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Knauf (Friedrich-Alexander-Universität Erlangen-Nürnberg
)
DTSTART:20200624T150000Z
DTEND:20200624T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/8
DESCRIPTION:Title: Asymptotic velocity for scattering particles\nby Andreas Knauf
(Friedrich-Alexander-Universität Erlangen-Nürnberg) as part of DinAmicI
: Another Internet Seminar\n\n\nAbstract\nPartly with Jacques Fejoz\, Rich
ard Montgomery\, Stefan Fleischer and Manuel Quaschner.\n\nThe past and fu
ture of scattering particle systems is partly determined by their asymptot
ic velocity\, that is\, the Cesàro limit of the velocity. That this exist
s for bounded interactions and all initial conditions\, is part of a state
ment sometimes called ‘asymptotic completeness’. The same statement do
es not apply to individual initial conditions in celestial mechanics. Howe
ver\, at least for up to four particles\, nonexistence of asymptotic veloc
ity is a measure zero phenomenon. We explain some new ideas connected with
the proof (Poincaré section techniques for wandering sets\, non-determin
istic particle systems\, and walks on a poset of set partitions).\n\nZoom
link: https://unipd.zoom.us/j/96933860238?pwd=c1pEamVCOVJNci9MVThZWWlzeGt6
UT09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Françoise Pène (Université de Bretagne Occidentale (France))
DTSTART:20200708T150000Z
DTEND:20200708T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/9
DESCRIPTION:Title: Invariance by induction of the asymptotic variance\nby Franço
ise Pène (Université de Bretagne Occidentale (France)) as part of DinAmi
cI: Another Internet Seminar\n\n\nAbstract\nIt is well known that the inte
gral of an observable is preserved by induction. We are interested here in
extensions of this result to moments of order 2 and 3. We have two natura
l candidates for the second and third order moments: the classical asympto
tic variance (given by the Green-Kubo formula) and an analogous quantity o
f the third order. This question arises from the proof of CLT. In some cas
es\, the asymptotic variance in the CLT can be expressed on the one hand i
n terms of the classical Green-Kubo formula and on the other hand in terms
of the Green-Kubo formula for the induced system. Under general assumptio
ns (involving transfer operators)\, we prove that the asymptotic variance
is preserved by induction and that the natural third order quantity is pre
served up to an error term.\n\nThis is joint work with Damien Thomine.\n\n
zoom link: https://unipd.zoom.us/j/95330010741?pwd=ZXBpejY0ZUNiQUVkdXFrcnF
0RW81UT09\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Marò (University of Pisa (Italy))
DTSTART:20201112T150000Z
DTEND:20201112T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/10
DESCRIPTION:Title: Chaotic motion in the breathing circle billiard\nby Stefano M
arò (University of Pisa (Italy)) as part of DinAmicI: Another Internet Se
minar\n\n\nAbstract\nWe consider the free motion of a point particle insid
e a circular billiard with periodically moving boundary\, with the assumpt
ion that the collisions of the particle with the boundary are elastic so t
hat the energy of the particle is not preserved. It is known that if the m
otion of the boundary is regular enough then the energy is bounded due to
the existence of invariant curves. We show that it is nevertheless possibl
e that the motion of the particle is chaotic\, also under regularity assum
ptions for the moving boundary. More precisely\, we show that there exists
a class of functions describing the motion of the boundary for which the
billiard map admits invariant probability measures with positive metric en
tropy. The proof relies on variational techniques based on Aubry-Mather th
eory. \nJoint work with Claudio Bonanno.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaia Nisoli (Universidade Federal do Rio de Janeiro (Brazil))
DTSTART:20201116T130000Z
DTEND:20201116T140000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/11
DESCRIPTION:Title: A simple system presenting Noise Induced Order\nby Isaia Niso
li (Universidade Federal do Rio de Janeiro (Brazil)) as part of DinAmicI:
Another Internet Seminar\n\n\nAbstract\nIn this talk I will present a fami
ly of one dimensional systems with random additive noise such that\, as th
e noise size increases\, the Lyapunov exponent of the stationary measure t
ransitions from positive to negative. This phenomena is known in literatur
e as Noise Induced Order\, and was first observed in a model of the Beloso
uv-Zhabotinsky reaction and its existence was proven only recently by Gala
tolo-Monge-Nisoli. In the talk I will show how this phenomena is strictly
connected with non-uniform hyperbolicity and the coexistence of regions of
expansion and contraction in phase space\; the result is attained through
a result on the continuity of the Lyapunov exponent of the stationary mea
sure with respect to the size of the noise.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (University of Rome Tor Vergata (Italy))
DTSTART:20201210T150000Z
DTEND:20201210T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/12
DESCRIPTION:Title: Locating Ruelle-Pollicott resonances\nby Carlangelo Liverani
(University of Rome Tor Vergata (Italy)) as part of DinAmicI: Another Inte
rnet Seminar\n\n\nAbstract\nWe study the spectrum of transfer operators as
sociated to various dynamical systems. Our aim is to obtain precise inform
ation on discrete spectrum. To this end we propose a unitary approach. We
consider various settings where new information can be obtained following
different branches along the proposed path. These settings include affine
expanding Markov maps\, uniformly expanding Markov maps\, non-uniformly ex
panding maps\, hyperbolic diffeomorphisms. We believe this to be the germ
of a general theory. Joint work with O. Butterley and N. Kiamari.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Miriam Benini (University of Parma (Italy))
DTSTART:20201126T160000Z
DTEND:20201126T170000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/13
DESCRIPTION:Title: Infinite entropy for transcendental entire functions\nby Anna
Miriam Benini (University of Parma (Italy)) as part of DinAmicI: Another
Internet Seminar\n\n\nAbstract\nDefining entropy on noncompact metric spac
es is a tricky business\, since there are several natural and nonequivalen
t generalizations of the usual notions of entropy for continuous maps on c
ompact spaces. By defining entropy for transcendental maps on the complex
plane as the sup over the entropy restricted to compact forward invariant
subsets\, we prove that with this definition the entropy of such functions
is infinite. The proof relies on covering results which are distinctive t
o holomorphic maps.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Venturelli (Université d'Avignon (France))
DTSTART:20210114T150000Z
DTEND:20210114T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/14
DESCRIPTION:Title: Hyperbolic motion in the Newtonian N-body problem with arbitrary
limit shape\nby Andrea Venturelli (Université d'Avignon (France)) as
part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nWe prove for the
N-body problem the existence of hyperbolic motions for any prescribed lim
it shape and any given initial configuration of the bodies. The energy lev
el h>0 of the motion can also be chosen arbitrarily. Our approach is based
on the construction of a global viscosity solutions for the Hamilton-Jaco
bi equation H(x\,du(x))=h. Our hyperbolic motion is in fact a calibrating
curve of the viscosity solution. The presented results can also be viewed
as a new application of Marchal’s theorem\, whose main use in recent lit
erature has been to prove the existence of periodic orbits. Joint work wit
h Ezequiel Maderna.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Gianfelice (Università della Calabria (Italy))
DTSTART:20210128T150000Z
DTEND:20210128T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/15
DESCRIPTION:Title: Stochastic stability of classical Lorenz flow under impulsive typ
e forcing\nby Michele Gianfelice (Università della Calabria (Italy))
as part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nInspired by t
he problem of modeling the so called anthropogenic forcing in climatology\
, e.g. the effects of the emissions of greenhouse gases in the atmosphere\
, we introduce a novel type of random perturbation for the classical Loren
z flow and prove its stochastic stability. The perturbation acts on the sy
stem in an impulsive way\, hence is not of diffusive type. Namely\, given
a cross-section M for the unperturbed flow\, each time the trajectory of t
he system crosses M the phase velocity field is changed with a new one sam
pled at random from a suitable neighborhood of the unperturbed one. The re
sulting random evolution is therefore described by a piecewise determinist
ic Markov process. The proof of the stochastic stability for the unperturb
ed flow is then carried on working either in the framework of the Random D
ynamical Systems or in that of semi-Markov processes. Joint work with Sand
ro Vaienti.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gary Froyland (University of New South Wale)
DTSTART:20210204T090000Z
DTEND:20210204T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/16
DESCRIPTION:Title: The dynamic ocean\nby Gary Froyland (University of New South
Wale) as part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nThe cir
culation of our oceans strongly influences climate\, weather and biology.
Our ocean currents are dynamic\, and fluctuate to varying extents. I will
introduce data-driven numerical tools that can tease apart dynamic compone
nts of the ocean\, with information sourced from ocean drifters\, satellit
e imagery\, and ocean models. These components\, their lifecycles\, and th
eir response to external forcing\, help us to build a dynamic picture of o
ur ocean.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Bialy (Tel Aviv University)
DTSTART:20210211T150000Z
DTEND:20210211T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/17
DESCRIPTION:Title: Birkhoff-Poritsky conjecture for centrally-symmetric billiards\nby Misha Bialy (Tel Aviv University) as part of DinAmicI: Another Inter
net Seminar\n\n\nAbstract\nIn this talk I shall discuss Birkhoff-Poritsky
conjecture for centrally-symmetric $C^2$-smooth convex planar billiards. \
n\nWe assume that the domain $\\mathcal A$ between the invariant curve of
$4$-periodic orbits and the boundary of the phase cylinder is foliated by
$C^0$-invariant curves. \nUnder this assumption we prove that the billiar
d curve is an ellipse.\nOther versions of Birkhoff-Poritsky conjecture fol
low from this result. \nFor the original Birkhoff-Poritsky formulation we
show that if a neighborhood of the boundary of billiard domain has\na $C^1
$-smooth foliation by convex caustics of rotation numbers in the interval
(0\; 1/4]\nthen the boundary curve is an ellipse. \n\nThe main ingredients
of the proof are:\n\n \n(1) the non-standard generating function for conv
ex billiards\; \n\n(2) the remarkable structure of the invariant curve co
nsisting of $4$-periodic orbits\; and\n\n \n(3) the integral-geometry appr
oach initiated in\n\\cite{B0}\, \\cite{B1} for rigidity results of circula
r billiards. \n\n\nSurprisingly\, we establish a Hopf-type rigidity for bi
lliards in the ellipse.\nBased on a joint work with Andrey E. Mironov (Nov
osibirsk).\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Giulietti (Università di Pisa)
DTSTART:20210225T150000Z
DTEND:20210225T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/18
DESCRIPTION:Title: Infinite mixing for accessible skew products\nby Paolo Giulie
tti (Università di Pisa) as part of DinAmicI: Another Internet Seminar\n\
n\nAbstract\nI will present some decay of correlations results on skew pro
ducts which are locally accessible. The results rely on the study of a twi
sted transfer operator and could be generalized to many other situations.
I will also present numerical counterparts to such results.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro del Pino Gómez (Utrecht University (The Netherlands))
DTSTART:20210325T150000Z
DTEND:20210325T160000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/19
DESCRIPTION:Title: Billiards in subriemannian geometry\nby Álvaro del Pino Góm
ez (Utrecht University (The Netherlands)) as part of DinAmicI: Another Int
ernet Seminar\n\n\nAbstract\nWhen one considers manifolds with boundary\,
billiard dynamics are the natural analogue of standard geodesic dynamics.
Namely\, instead of having geodesics escape at the boundary\, we force the
m back into the manifold using the reflection law. In other dynamical sett
ings\, similar constructions are possible: In 2006\, B. Khesin and S. Taba
chnikov initiated the study of billiards in the semiriemannian setting\, s
tudying the integrability of various tables. In recent years we have also
seen the appearance of several billiard setups of symplectic nature.\n\nIn
this talk I will discuss recent work with L. Dahinden in which we look at
billiards in subriemannian geometry. I will sketch how the reflection law
arises naturally both from the control-theoretical and symplectic perspec
tives\, how the reflection is problematic at tangency points between the d
istribution and the boundary of the table\, and I will introduce some conc
rete examples. My ultimate goal will be to pose several intriguing open qu
estions.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda & Daniel Peralta-Salas (UPC Barcelona & ICMAT Madrid (
Spain))
DTSTART:20210408T140000Z
DTEND:20210408T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/20
DESCRIPTION:Title: Looking at Euler flows through a contact mirror: Universality and
Turing completeness\nby Eva Miranda & Daniel Peralta-Salas (UPC Barce
lona & ICMAT Madrid (Spain)) as part of DinAmicI: Another Internet Seminar
\n\n\nAbstract\nThe dynamics of an inviscid and incompressible fluid flow
on a Riemannian manifold is governed by the Euler equations. Recently\, Ta
o launched a programme to address the global existence problem for the Eul
er and Navier Stokes equations based on the concept of universality. Inspi
red by this proposal\, we show that the stationary Euler equations exhibit
several universality features\, In the sense that\, any non-autonomous fl
ow on a compact manifold can be extended to a smooth stationary solution o
f the Euler equations on some Riemannian manifold of possibly higher dimen
sion. \nThese results can be viewed as lending support to the intuition th
at solutions to the Euler equations can be extremely complicated in nature
.\nA key point in the proof is looking at the h-principle in contact geome
try through a contact mirror\, unveiled by Sullivan\, Etnyre and Ghrist mo
re than two decades ago.\n\nWe end up this talk addressing an apparently d
ifferent question: What kind of physics might be non-computational? Using
the former universality result\, we can establish the Turing completeness
of the steady Euler flows\, i.e.\, there exist solutions that encode a uni
versal Turing machine and\, in particular\, these solutions have undecida
ble trajectories.. But\, in view of the increase of dimension yielded by o
ur proof. The question is can this be done in dimension 3? We will prove t
he existence of Turing complete fluid\nflows on a 3-dimensional geometric
domain. Our novel strategy uses the computational power of symbolic dynami
cs and the contact mirror again.\n\nThis talk is based on joint work with
Robert Cardona and Fran Presas ( arXiv:1911.01963 and arXiv:2012.12828 )\
n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Della Corte (Università di Camerino (Italy))
DTSTART:20210311T160000Z
DTEND:20210311T170000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/21
DESCRIPTION:Title: The simplest erasing substitution\nby Alessandro Della Corte
(Università di Camerino (Italy)) as part of DinAmicI: Another Internet Se
minar\n\n\nAbstract\nThe symbolic action of a substitution on the binary e
xpansion generates naturally an interval map. In case of erasing substitut
ions\, the map is typically Baire-1 and not Darboux. As a model case\, we
consider what is arguably the simplest erasing substitution\, mapping 0s t
o the empty word and 1s to 0 or 1 depending on the parity. The correspondi
ng interval map is shown to have fractal properties (bounds are given on t
he Hausdorff dimension of the fibers) and to display rich dynamical behavi
or\, including Devaney chaos\, uniform distributional chaos of type 1\, in
finite topological entropy as well as the presence of cycles attracting in
a finite time every rational.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanja Schindler (Scuola Normale Superiore di Pisa (Italy))
DTSTART:20210422T140000Z
DTEND:20210422T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/22
DESCRIPTION:Title: Almost sure asymptotic behaviour of Birkhoff sums for infinite me
asure-preserving dynamical systems\nby Tanja Schindler (Scuola Normale
Superiore di Pisa (Italy)) as part of DinAmicI: Another Internet Seminar\
n\n\nAbstract\nWe are interested in the limit behaviour of Birkhoff sums o
ver an infinite sigma-finite measure space. If the observable is integrabl
e then — by a classical theorem by Aaronson — there exists no sequence
of real numbers such that the Birkhoff sum normed by this sequence conver
ges almost surely to 1. Under strong mixing conditions on the underlying s
ystem we prove a generalized strong law of large numbers for integrable ob
servables using a truncated sum adding a suitable number of terms dependin
g on the point of evaluation. For f not integrable we give conditions on f
such that the Birkhoff sum normed by a sequence of real numbers converges
almost surely to 1. Joint work with Claudio Bonanno.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selim Ghazouani (Université Paris-Sud (France))
DTSTART:20210506T140000Z
DTEND:20210506T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/23
DESCRIPTION:Title: Piecewise affine homeomorphisms of the circle and dilation surfac
es\nby Selim Ghazouani (Université Paris-Sud (France)) as part of Din
AmicI: Another Internet Seminar\n\n\nAbstract\nIn this talk I will conside
r the following question: if one picks a piecewise affine map of the circl
e “at random”\, what dynamical behaviour are we likely to observe? The
case of standard circle diffeomorphisms has been studied by Herman in the
80s\; in this emblematic case the problem can be reduced to theorems clos
e to KAM theory. For the piecewise affine case\, we put forward a geometri
c approach\, inspired by methods from both Teichmüller theory and hyperbo
lic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Zannier (Scuola Normale Superiore di Pisa (Italy))
DTSTART:20210520T140000Z
DTEND:20210520T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/24
DESCRIPTION:Title: Torsion values of sections\, elliptical billiards and diophantine
problems in dynamics\nby Umberto Zannier (Scuola Normale Superiore di
Pisa (Italy)) as part of DinAmicI: Another Internet Seminar\n\n\nAbstract
\nAfter a very brief review of basics on elliptic curves and their familie
s\, we shall consider "sections" of such families\, and especially their
"torsion values". For instance\, what can be said of the complex numbers b
for which (2\, \\sqrt{2(2-b)}) is torsion on the Legendre curve y^2=x(x-1
)(x-b)? In particular\, we shall recall results of "Manin-Mumford type" an
d focus to illustrate some applications to elliptical billiards. Finally\,
if time allows we shall frame these issues as special cases of a general
question in arithmetic dynamics\, which can be treated with different meth
ods\, depending on the context.\n(Most results refer to work with Pietro C
orvaja and David Masser.)\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tanzi (New York University (USA))
DTSTART:20210604T140000Z
DTEND:20210604T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/25
DESCRIPTION:Title: Random-like properties of chaotic forcing\nby Matteo Tanzi (N
ew York University (USA)) as part of DinAmicI: Another Internet Seminar\n\
n\nAbstract\nWe prove that skew systems with a sufficiently expanding base
have “approximate” statistical properties similar to random ergodic M
arkov chains. For example\, they exhibit approximate exponential decay of
correlations\, meaning that the exponential rate is observed modulo a cont
rolled error. The fiber maps are only assumed to be Lipschitz regular and
to depend on the base in a way that guarantees diffusive behaviour on the
vertical component. The assumptions do not imply an hyperbolic picture and
one cannot rely on the spectral properties of the transfer operators invo
lved. The approximate nature of the result is the inevitable price one pay
s for having so mild assumptions on the dynamics on the vertical component
. The error in the approximation is shown to go to zero when the expansion
of the base tends to infinity.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Artigiani (Universidad del Rosario (Colombia))
DTSTART:20210617T140000Z
DTEND:20210617T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/26
DESCRIPTION:Title: Double rotations and their ergodic properties\nby Mauro Artig
iani (Universidad del Rosario (Colombia)) as part of DinAmicI: Another Int
ernet Seminar\n\n\nAbstract\nDouble rotations are the simplest subclass of
interval translation mappings. A double rotation is of finite type if its
attractor is an interval and of infinite type if it is a Cantor set. It i
s easy to see that the restriction of a double rotation of finite type to
its attractor is simply a rotation. It is known due to Suzuki - Ito - Aiha
ra and Bruin - Clark that double rotations of infinite type are defined by
a subset of zero measure in the parameter set. We introduce a new renorma
lization procedure on double rotations\, which is reminiscent of the class
ical Rauzy induction. Using this renormalization\, we prove that the set o
f parameters which induce infinite type double rotations has Hausdorff dim
ension strictly smaller than 3. Moreover\, we construct a natural invarian
t measure supported on these parameters and show that\, with respect to th
is measure\, almost all double rotations are uniquely ergodic. In my talk
I plan to outline this proof that is based on the recent result by Fougero
n for simplicial systems. I also hope to discuss briefly some challenging
open questions and further research plans related to double rotations.\n\n
The talk is based on a joint work with Charles Fougeron\, Pascal Hubert an
d Sasha Skripchenko.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasun Fernando (University of Toronto (Canada))
DTSTART:20210624T140000Z
DTEND:20210624T150000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/27
DESCRIPTION:Title: Expansions in the mixing local limit theorems for dynamical syste
ms\nby Kasun Fernando (University of Toronto (Canada)) as part of DinA
micI: Another Internet Seminar\n\n\nAbstract\nIn this talk\, we introduce
higher-order expansions in the mixing local limit theorems for Birkhoff su
ms. We will discuss the general results under technical assumptions\, and
illustrate them by different examples (e.g. subshifts of finite type\, You
ng towers\, Sinai billiards\, and random matrix products)\, including situ
ations of unbounded observables with integrability order arbitrarily close
to the optimal moment condition required in the i.i.d. setting. This is j
oint work with Françoise Pène.\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanja I. Schindler & Jon Aaronson (Jagiellonian University & Tel A
viv University)
DTSTART:20240605T140000Z
DTEND:20240605T153000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/28
DESCRIPTION:Title: "Properties and limit laws of dynamical systems with two infinite
components" & "Open problems in Infinite Ergodic Theory"\nby Tanja I.
Schindler & Jon Aaronson (Jagiellonian University & Tel Aviv University)
as part of DinAmicI: Another Internet Seminar\n\n\nAbstract\nFirst talk: W
hile studying dynamical systems with one infinite component\, i.e. a proba
bility preserving dynamical system and a non-integrable observable or an i
nfinite measure preserving dynamical system with an integrable observable
still has a lot of interesting questions - it is interesting to study syst
ems with more than one infinite component. An example would be an infinite
measure system with an observable which is not integrable on a finite mea
sure set. Another example would be a dynamical system with two dynamically
separated infinite measure sets A and B\; i.e. orbits have to pass throug
h a finite measure set Y in order to pass from A to B and vice versa. I wi
ll show some (completely incomplete list of) examples where one of the abo
ve described behaviours occur. This is a somewhat expository talk includin
g joint work with Claudio Bonanno and Muhammad Mubarak.\n\nSecond talk:\n\
nFor the link check https://www.dinamici.org/dai-seminars/2024-06-schindle
r-aaronson/\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Kanigowski & Kosma Kasprzak (University of Maryland & Jagiell
onian University\, Krakow)
DTSTART:20241001T140000Z
DTEND:20241001T153000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/29
DESCRIPTION:Title: "Ergodic Theorems along sparse subsets of the integers" & "Ergodi
city along square orbits in rigid dynamical systems"\nby Adam Kanigows
ki & Kosma Kasprzak (University of Maryland & Jagiellonian University\, Kr
akow) as part of DinAmicI: Another Internet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacopo De Simoi & Carlangelo Liverani (University of Toronto & Uni
versità di Roma Tor Vergata)
DTSTART:20241203T150000Z
DTEND:20241203T163000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/30
DESCRIPTION:Title: "Statistical properties of some mostly expanding fast-slow partia
lly hyperbolic systems" & "Some open problems and considerations at the in
tersection of partially hyperbolic systems\, randomness\, and statistical
mechanics"\nby Jacopo De Simoi & Carlangelo Liverani (University of To
ronto & Università di Roma Tor Vergata) as part of DinAmicI: Another Inte
rnet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lai-Sang Young & Kevin K Lin (CIMS\, New York University & Univers
ity of Arizona)
DTSTART:20250204T150000Z
DTEND:20250204T163000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/31
DESCRIPTION:Title: "Dynamics of the visual system" & "Coarse-grained modeling of the
primary visual cortex"\nby Lai-Sang Young & Kevin K Lin (CIMS\, New Y
ork University & University of Arizona) as part of DinAmicI: Another Inter
net Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Canestrari & Wael Bahsoun (Università di Bologna & Lough
borough University)
DTSTART:20250408T140000Z
DTEND:20250408T153000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/33
DESCRIPTION:Title: "Linear response: from physics to dynamical systems and back" & "
Linear response due to singularities"\nby Giovanni Canestrari & Wael B
ahsoun (Università di Bologna & Loughborough University) as part of DinAm
icI: Another Internet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Marmi & Matteo Tanzi (Scuola Normale Superiore Pisa & King
's College London)
DTSTART:20251009T140000Z
DTEND:20251009T153000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/34
DESCRIPTION:Title: "Why are dynamical systems and ergodic theory relevant to economi
cs and finance?" & "Leverage Dynamics in Banks Interacting through an Asse
t"\nby Stefano Marmi & Matteo Tanzi (Scuola Normale Superiore Pisa & K
ing's College London) as part of DinAmicI: Another Internet Seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paulo Varandas & Nicola Bertozzi (Universidade de Aveiro & Univers
ità di Pisa)
DTSTART:20260211T150000Z
DTEND:20260211T163000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/35
DESCRIPTION:Title: "On the decay of correlations for codimension-one hyperbolic attr
actors" & "Exponential decay of correlations for two families of suspensio
n flows over non-compact spaces"\nby Paulo Varandas & Nicola Bertozzi
(Universidade de Aveiro & Università di Pisa) as part of DinAmicI: Anothe
r Internet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elise Goujard & Magali Jay (Nantes Université & Max Planck Instit
ute Leipzig)
DTSTART:20251209T150000Z
DTEND:20251209T163000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/36
DESCRIPTION:Title: "An introduction to dynamics of polygonal billiards" & "Tiling bi
lliard in the wind-tree model"\nby Elise Goujard & Magali Jay (Nantes
Université & Max Planck Institute Leipzig) as part of DinAmicI: Another I
nternet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tere M-Seara & Jaime Paradela Diaz (Universitat Politècnica de Ca
talunya & University of Maryland)
DTSTART:20240508T140000Z
DTEND:20240508T153000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/37
DESCRIPTION:Title: "Unstable motions in the Three Body Problem" & "Homoclinic tangen
cies of parabolic saddles and Newhouse domains in Celestial Mechanics"
\nby Tere M-Seara & Jaime Paradela Diaz (Universitat Politècnica de Catal
unya & University of Maryland) as part of DinAmicI: Another Internet Semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Melbourne & Douglas Coates (University of Warwick & Universida
de Federal do Rio de Janeiro)
DTSTART:20260310T150000Z
DTEND:20260310T163000Z
DTSTAMP:20260404T111415Z
UID:DinAmicI/38
DESCRIPTION:Title: "Mixing for infinite measure systems" & "Global-local mixing for
intermittent maps"\nby Ian Melbourne & Douglas Coates (University of W
arwick & Universidade Federal do Rio de Janeiro) as part of DinAmicI: Anot
her Internet Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DinAmicI/38/
END:VEVENT
END:VCALENDAR