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BEGIN:VEVENT
SUMMARY:Olga Lukina (University of Vienna)
DTSTART:20200424T081500Z
DTEND:20200424T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/1
DESCRIPTION:Title: Stabilizers in group Cantor actions and measures\nby Olga Lukina
(University of Vienna) as part of Dynamical systems seminar at the Jagiell
onian University\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Roth (Silesian University)
DTSTART:20200515T081500Z
DTEND:20200515T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/2
DESCRIPTION:Title: Special alpha-limit sets on the interval\nby Samuel Roth (Silesia
n University) as part of Dynamical systems seminar at the Jagiellonian Uni
versity\n\nLecture held in 1016.\n\nAbstract\nFor a noninvertible dynamica
l system (X\,f) a point x can have many\npossible “pasts.” Special alp
ha limit sets were defined to contain all\nthe limit points of all those b
ackward orbits\, and it turns out that for\ninterval maps they have many g
ood properties. For example\, a point\nbelongs to its own special alpha li
mit set (this is like “backward\nrecurrence”) if and only if it is in
the attracting center of the interval\nmap [Hero\, 1992].\n\nOne of the la
st papers by Sergei Kolyada proposes several conjectures\nand open problem
s about topological properties of special-alpha limit\nsets. This talk wil
l address those problems. The project is joint work\nwith Jana Hantáková
.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Kwietniak
DTSTART:20200508T081500Z
DTEND:20200508T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/3
DESCRIPTION:Title: Entropy\, f-bar\, and Abramov's formula for the entropy of induced tr
ansformations\nby Dominik Kwietniak as part of Dynamical systems semin
ar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nRe
call that an infinite sequence over a finite alphabet A is\nquasi-regular\
, if it is a generic point for a (non-necessarily\nergodic) shift-invarian
t measure. Given a quasi-regular point x in the\nfull shift over A we writ
e h(x) for the Kolmogorov-Sinai entropy of\nthe shift invariant Borel prob
ability measure generated by x. We prove\nthat h is uniformly continuous o
n the set of all quasi-regular points\nendowed with the f-bar (pseudo)dist
ance. We also give an alternative\nproof of Abramov's formula for the entr
opy of induced transformations.\nThis is a joint work with Tomasz Downarow
icz and Martha Łącka.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Misiurewicz (IUPUI)
DTSTART:20200522T141500Z
DTEND:20200522T154500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/4
DESCRIPTION:Title: Flexibility of entropies for piecewise expanding unimodal maps\nb
y Michał Misiurewicz (IUPUI) as part of Dynamical systems seminar at the
Jagiellonian University\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Fuhrmann (Imperial College London)
DTSTART:20200605T081500Z
DTEND:20200605T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/5
DESCRIPTION:Title: Some recent progress on tameness in minimal systems\nby Gabriel F
uhrmann (Imperial College London) as part of Dynamical systems seminar at
the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nTameness
is a notion which--very roughly speaking--refers to the\nabsence of topol
ogical complexity of a dynamical system. The last\ndecades saw an increase
d interest in tame systems revealing their\nconnections to other areas of
mathematics like Banach spaces\,\nsubstitutions and tilings or even model
theory and logic. In this\ntalk\, we will assume a dynamical systems persp
ective.\n\nHuang showed that\, given a minimal system\, tameness implies a
lmost\nautomorphy [1]. That is\, after discarding a meagre set of points\,
the\nfactor map of a tame minimal system to its maximal equicontinuous\nf
actor is one-to-one. This structural theorem got recently extended to\nact
ions of general groups by Glasner [2].\n\nIn a collaboration with Glasner\
, Jäger and Oertel\, we could further\nimprove this result by showing tha
t tame minimal systems are actually\nregularly almost automorphic [3]. In
this talk\, we will show a closely\nrelated statement which\, however\, is
way easier to prove: every\nsymbolic almost automorphic extension of an i
rrational rotation whose\nnon-invertible fibres form a Cantor set is non-t
ame. We will further\ndiscuss some related results from a collaboration wi
th Kwietniak [4].\nFinally\, if time allows\, we will come to discuss tame
ness in\nsubstitutive subshifts and more general classes of Toeplitz flows
[5].\n\nAll (non-standard) notions will be introduced in the talk. In oth
er\nwords: we prioritise accessibility over the number of results to be\nd
iscussed.\n\n[1] W. Huang\, Tame systems and scrambled pairs under an abel
ian group\naction\, Ergodic Theory Dynam. Systems 26 (2006)\, 1549-1567.\n
\n[2] E. Glasner\, The structure of tame minimal dynamical systems for\nge
neral groups\, Invent. Math. 211 (2018)\, 213-244.\n\n[3] G. Fuhrmann\, E.
Glasner\, T. Jäger\, C. Oertel\, Irregular model sets\nand tame dynamics
\, arXiv:1811.06283\, (2018)\, 1-22.\n\n[4] G. Fuhrmann\, D. Kwietniak\, O
n tameness of almost automorphic\ndynamical systems for general groups\, B
ull. Lon. Math. Soc. 52 (2020)\,\n24-42.\n\n[5] G. Fuhrmann\, J. Kellendon
k\, R. Yassawi\, work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Oertel-Jäger (Friedrich Schiller University Jena)
DTSTART:20200529T081500Z
DTEND:20200529T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/6
DESCRIPTION:Title: Topological dynamics of irregular model sets\nby Tobias Oertel-J
äger (Friedrich Schiller University Jena) as part of Dynamical systems se
minar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\
nModel sets have been introduced by Yves Meyer in 1972. As\nthe underlying
cut and project schemes present a quite general method\nto construct aper
iodic point-sets with long-range order\, they are\noften studied in the th
eory of mathematical quasicrystals. At the same\ntime\, they present an in
teresting class of examples in the context of\ntopological dynamics.\n\nIn
this talk\, we will concentrate on the dynamics of so-called\nirregular m
odel sets\, whose dynamics are generally more complicated\nand less unders
tood than that of regular models (like the Fibonacci\nquasicrystal). We sh
ow that the Delone dynamical systems associated to\nirregular model sets o
ften show positive entropy\, but the construction\nalso allows for uniquel
y ergodic zero entropy examples. However\,\nirregular models sets cannot b
e tame\, which provides a lower bound for\nthe complexity of their dynamic
s.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny (Einstein Institute of Mathematics\, UJ)
DTSTART:20200612T081500Z
DTEND:20200612T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/7
DESCRIPTION:Title: Automatic multiplicative sequences\nby Jakub Konieczny (Einstein
Institute of Mathematics\, UJ) as part of Dynamical systems seminar at the
Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nAutomatic s
equences - that is\, sequences computable by\nfinite automata - give rise
to one of the most basic models of\ncomputation. As such\, for any class o
f sequences it is natural to ask\nwhich sequences in it are automatic. In
particular\, the question of\nclassifying automatic multiplicative sequenc
es has attracted\nconsiderable attention in recent years. In the completel
y\nmultiplicative case\, such classification was obtained independently by
\nS. Li and O. Klurman and P. Kurlberg. The main topic of my talk will\nbe
the resolution of the general case\, obtained in a recent preprint\nwith
M. Lemańczyk and C. Müllner.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Melleray (Institut Camille Jordan\, Université Lyon 1)
DTSTART:20200619T081500Z
DTEND:20200619T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/8
DESCRIPTION:Title: Characterizing sets of invariant probability measures of minimal home
omorphisms of the Cantor space\nby Julien Melleray (Institut Camille J
ordan\, Université Lyon 1) as part of Dynamical systems seminar at the Ja
giellonian University\n\nLecture held in 1016.\n\nAbstract\nGiven a set K
of probability measures on a Cantor set X\, one\ncan ask whether there exi
sts a minimal homeomorphism (= all orbits are\ndense) whose invariant prob
ability measures are exactly the elements of\nK. We say that K is a dynami
cal simplex if such a homeomorphism exists\;\nI will present a characteriz
ation of dynamical simplices\, which is based\nin large part on work of T.
Ibarlucia and myself\; and try to explain the\nproof strategy\, based on
the notion of Kakutani-Rokhlin partitions. The\ntalk will be introductory
in nature and not assume prior knowledge of\nCantor dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Kwietniak (Jagiellonian University)
DTSTART:20201002T081500Z
DTEND:20201002T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/9
DESCRIPTION:Title: Dbar-approachability\, entropy density and B-free shifts\nby Domi
nik Kwietniak (Jagiellonian University) as part of Dynamical systems semin
ar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nWe
study which properties of shift spaces transfer to their Hausdorff\nmetri
c dbar-limits. In particular\, we study shift spaces we call\ndbar-approac
hable\, which are Hausdorff metric dbar-limits of their own\nk-step Markov
approximations. We provide a topological\ncharacterisation of chain mixin
g dbar-approachable shift spaces using\nthe dbar-shadowing property. This
can be considered as an analogue for\nFriedman and Ornstein's characterisa
tion of Bernoulli processes. We\nprove that many classical specification p
roperties imply chain mixing\nand dbar-approachability. It follows that th
ere are tons of\ninteresting dbar-approachable shift spaces (mixing shifts
of finite\ntype\, or more generally mixing sofic shifts\, or even more ge
nerally\,\nshift spaces with the specification or beta-shifts. In addition
\, we\nconstruct minimal and proximal examples of dbar-approachable shift\
nspaces\, thus proving dbar-approachability is a more general phenomenon\n
than specification. We also show that dbar-approachability and\nchain-mixi
ng imply dbar-stability\, a property recently introduced by\nTim Austin in
his study of Bernoulliness of equilibrium states. This\nallows us to prov
ide first examples of minimal or proximal dbar-stable\nshift spaces\, thus
answering a question posed by Austin. Finally\, we\nshow that the set of
shift spaces with entropy-dense ergodic measures\nis closed wrt dbar Haus
dorff metric. Note that entropy-density of\nergodic measures is known to h
old for many classes of shift spaces\nwith variants of the specification p
roperty\, but our result show that\nin these cases the entropy-density is
a mere consequence of\nentropy-density of mixing shifts of finite type and
\ndbar-approachability. Since we know there are examples of minimal or\npr
oximal dbar-approachable shifts\, we see that our technique yields\nentrop
y-density for examples which were beyond the reach of methods\nbased on sp
ecification properties. Finally\, we apply our technique to\nhereditary cl
osures of B-free shifts (a class including many\ninteresting B-free shifts
). These shift spaces are not chain-mixing\,\nhence they are not dbar-appr
oachable\, but they are easily seen to be\napproximated by naturally defin
ed sequences of transitive sofic\nshifts\, and this implies entropy-densit
y. This is a joint work with\nJakub Konieczny and Michal Kupsa.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joanna Kułaga-Przymus (UMK Toruń)
DTSTART:20201009T081500Z
DTEND:20201009T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/10
DESCRIPTION:Title: Entropy rate of product of independent processes\nby Joanna Kuł
aga-Przymus (UMK Toruń) as part of Dynamical systems seminar at the Jagie
llonian University\n\nLecture held in 1016.\n\nAbstract\nThe entropy of th
e product of stationary processes is related to\nFurstenberg’s filtering
problem. In its classical version one deals\nwith the sum $\\bm{X}+\\bm{Y
}$\, where $\\bm{X}$ corresponds to the signal\nand $\\bm{Y}$ to the noise
. In his seminal paper from 1967\, Furstenberg\nshowed that under the natu
ral assumption of the disjointness of\nunderlying dynamical systems\, the
information about $\\bm{X}$ can be\nretrieved from $\\bm{X}+\\bm{Y}$. Inst
ead of the sum\, we study the\nproduct $\\bm{X}\\cdot\\bm{Y}$. We give a f
ormula for the entropy rate of\n$\\bm{X}\\cdot\\bm{Y}$ (relative to that o
f $\\bm{Y}$\, for $\\bm{X}$ and\n$\\bm{Y}$ being independent). As a conseq
uence\, $\\bm{X}$ cannot be\nrecovered from $\\bm{X}\\cdot\\bm{Y}$ for a w
ide class of positive\nentropy processes\, including exchangeable processe
s\, Markov chains and\nweakly Bernoulli processes. Moreover\, we answer so
me open problems on\nthe dynamics of $\\mathscr{B}$-free systems (includin
g the square-free\nsystem given by the square of the Moebius function). Th
e talk is based\non joint work with Michał Lemańczyk\, see\nhttps://arxi
v.org/pdf/2004.07648.pdf\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Szczepanek
DTSTART:20201023T081500Z
DTEND:20201023T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/11
DESCRIPTION:Title: Dynamical Entropy of Unitary Operators in Finite-dimensional State S
paces\nby Anna Szczepanek as part of Dynamical systems seminar at the
Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nQuantum dyna
mical entropy quantifies the irreducible randomness of the sequences of ou
tcomes generated by a repetitively measured quantum system that between ea
ch two consecutive measurements is subject to unitary evolution. For sever
al classes of quantum measurements\, we derive an efficient formula for dy
namical entropy by establishing the limiting measure of the Markov chain g
enerated by the system and evaluating the Blackwell integral entropy formu
la. We also discuss the class of chaotic unitaries\, i.e.\, those with pot
ential to generate maximally random sequences of outcomes. Employing the n
otion of complex Hadamard matrices\, we give a necessary condition for cha
oticity (expressed in terms of the operator’s trace and determinant)\, w
hich in dimensions 2 and 3 is sufficient as well.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Byszewski
DTSTART:20201030T091500Z
DTEND:20201030T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/12
DESCRIPTION:Title: Arithmetic properties of the number of periodic points\nby Jakub
Byszewski as part of Dynamical systems seminar at the Jagiellonian Univer
sity\n\nLecture held in 1016.\n\nAbstract\nThe talk will be of expository
character and is based on a joint\nsurvey paper with Grzegorz Graff and Th
omas Ward. Given a dynamical\nsystem\, we may consider the sequence counti
ng the number of periodic\npoints of given order (if finite). (Equivalentl
y\, this information can\nbe given in terms of the dynamical zeta function
of the system.) We\nwill discuss some arithmetic properties of the class
of sequences that\ncan be obtained in this manner. Many of such results ha
ve been\nindependently rediscovered by various mathematicians working in\n
multiple fields.\n\nIn the latter part of the talk\, we will also discuss
some more recent\nresults concerning the growth rate of the number of peri
odic points in\ncertain systems of algebraic origin\, and obtained in a jo
int work with\nGunther Cornelissen and Marc Houben.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Downarowicz
DTSTART:20201106T091500Z
DTEND:20201106T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/13
DESCRIPTION:Title: Multiorder of countable groups\nby Tomasz Downarowicz as part of
Dynamical systems seminar at the Jagiellonian University\n\nLecture held
in 1016.\n\nAbstract\nI will present the notion of a Multiorder of a count
able group\,\na particular case of an Invariant Random Order introduced by
\nJohn Kieffer in 1975.\nI will discuss how multiorder is related to orbit
equivalence to\nZ-actions and I will prove that if the group is amenable
then\neach multiorder has the F\\o lner property. If time permits\, I will
\nalso show how to construct a uniformly F\\o lner multiorder of\nentropy
zero\, using a tiling system.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Hausner (FSU Jena)
DTSTART:20201127T091500Z
DTEND:20201127T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/14
DESCRIPTION:Title: Entropy in the context of aperiodic order\nby Till Hausner (FSU
Jena) as part of Dynamical systems seminar at the Jagiellonian University\
n\nLecture held in 1016.\n\nAbstract\nIn this talk we study different noti
ons of entropy for\nDelone sets of finite local complexity in the setting
of (metrizable\nand sigma-compact) locally compact Abelian groups (LCA gro
ups).\n\nFor Delone sets of finite local complexity (FLC) in the euclidean
\nspace it is well known that the patch counting entropy equals the\ntopol
ogical entropy of an associated shift system. We present an\nexample of a
FLC Delone set in a LCA group for which the topological\nentropy and the p
atch counting entropy are not equal.\n\nIt was suggested by J. Lagarias fo
r FLC Delone sets in the euclidean\nspace that the patch counting entropy
can always be computed as a\nlimit. We discuss why the Ornstein-Weiss lemm
a can not directly be\nused in order to see this claim and present that th
e correspondence\nbetween the topological and the patch counting entropy c
an be used in\norder to show that the limit in the patch counting entropy
formula\nexists for compactly generated LCA groups. We present counterexam
ples\nwhere the limit does not exist in the context of general LCA groups.
\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paulo Varandas (UFBA/Porto)
DTSTART:20201120T091500Z
DTEND:20201120T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/15
DESCRIPTION:Title: Phase transitions and appearance of ghost measures\nby Paulo Var
andas (UFBA/Porto) as part of Dynamical systems seminar at the Jagiellonia
n University\n\nLecture held in 1016.\n\nAbstract\nThe thermodynamic forma
lism for transitive uniformly\nhyperbolic dynamics is nowadays well unders
tood and\, among other\naspects\, it is worth mentioning that regular pote
ntials (meaning\nHolder continuous) are so that the pressure function is d
ifferentiable\nand admit unique equilibrium states. The situation changes
drastically\nin simple examples beyond uniform hyperbolicity\, as the case
of the\nManneville-Pomeau maps\, where different kinds of phase transitio
ns\nappear due to the phenomenon of intermittency of an indifferent fixed\
npoint. In this talk I will focus on this family and discuss a new\naspect
of the phase transitions\, namely the appearance of finitely\nadditive ab
solutely continuous invariant measures.In particular\, the\nsecond-order p
hase transition can be detected as a first-order phase\ntransition for an
extended pressure function. This is part of an\nongoing work with A. Castr
o (UFBA) and L. Cioletti (UnB).\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Wolf (CUNY)
DTSTART:20201204T140000Z
DTEND:20201204T150000Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/16
DESCRIPTION:Title: Computability of topological pressure on compact shift spaces beyond
finite type\nby Christian Wolf (CUNY) as part of Dynamical systems se
minar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\
nIn this talk we discuss the computability (in the sense of computable\nan
alysis) of the topological pressure $P_{\\rm top}(\\phi)$ on compact\nshif
t spaces $X$ for continuous potentials $\\phi:X\\to\\bR$. This\nquestion h
as recently been studied for subshifts of finite type (SFTs)\nand their fa
ctors (Sofic shifts). We develop a framework to address\nthe computability
of the topological pressure on general shift spaces\nand apply this frame
work to coded shifts. In particular\, we prove the\ncomputability of the t
opological pressure for all continuous\npotentials on S-gap shifts\, gener
alized gap shifts\, and Beta shifts.\nWe also construct shift spaces which
\, depending on the potential\,\nexhibit computability and non-computabili
ty of the topological\npressure. We further show that the generalized pres
sure function\n$(X\,\\phi)\\mapsto P_{\\rm top}(X\,\\phi\\vert_{X})$ is no
t computable for a\nlarge set of shift spaces $X$ and potentials $\\phi$.
Along the way of\ndeveloping these computability results\, we derive sever
al\nergodic-theoretical properties of coded shifts which are of\nindepende
nt interest beyond the realm of computability. The topic of\nthe talk is j
oint work with Michael Burr (Clemson U.)\, Shuddho Das\n(NYU) and Yun Yang
(Virginia Tech).\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Todd (St. Andrews)
DTSTART:20201211T091500Z
DTEND:20201211T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/17
DESCRIPTION:Title: Pressure on non-compact spaces\nby Mike Todd (St. Andrews) as pa
rt of Dynamical systems seminar at the Jagiellonian University\n\nLecture
held in 1016.\n\nAbstract\nThermodynamic formalism has a lot to say in the
context of\nsufficiently regular dynamical systems in compact spaces\, fo
r example\nabout the existence and uniqueness properties of equilibrium st
ates\,\nand their characterisation as some derivative of the pressure\nfun
ction. This talk considers non-compact settings\, particularly the\ncase
of countable Markov shifts. A first natural approach is to take\nthe comp
letion of the space and hope that the boundary created doesn’t\ninterfer
e with too many thermodynamic properties. I’ll look at how\none might d
o this\, some drawbacks\, and how they can\, in some cases\, be\novercome.
\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katrin Gelfert (UFRJ)
DTSTART:20201113T101500Z
DTEND:20201113T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/18
DESCRIPTION:Title: Heterodimensionality of skew-products with concave fiber maps\nb
y Katrin Gelfert (UFRJ) as part of Dynamical systems seminar at the Jagiel
lonian University\n\nLecture held in 1016.\n\nAbstract\nI will present som
e examples of skew-products with concave\ninterval fiber maps over a certa
in subshift. Here the subshift occurs\nas the projection of those orbits t
hat stay in a given neighborhood\nand gives rise to a new type of symbolic
space which is (essentially)\ncoded. The fiber maps have expanding and co
ntracting regions. As a\nconsequence\, the skew-product dynamics has pairs
of horseshoes of\ndifferent type of hyperbolicity. In some cases\, they d
ynamically\ninteract due to the superimposed effects of the (fiber) contra
ction\nand expansion\, leading to nonhyperbolic dynamics that is reflected
on\nthe ergodic level (existence of nonhyperbolic ergodic measures). The\
nspace of ergodic measures of the shift space is shown to be an\nentropy-d
ense Poulsen simplex\, ergodic measures lift canonically to\nergodic measu
res for the skew-product.\nSuch skew-products can be embedded in increasin
g entropy one-parameter\nfamily of diffeomorphisms which stretch from a he
terodimensional cycle\nto a collision of homoclinic classes. I will discus
s some ingredients\nof associated bifurcation phenomena that involve a jum
p of the space\nof ergodic measures and\, in some cases\, also of entropy.
(Joint work\nwith L.J.Díaz and M.Rams)\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Mroczek
DTSTART:20210108T091500Z
DTEND:20210108T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/19
DESCRIPTION:Title: The Besicovitch Metric on the Space of G -invariant Ergodic Measures
\nby Marcel Mroczek as part of Dynamical systems seminar at the Jagiel
lonian University\n\nLecture held in 1016.\n\nAbstract\nGiven two sequence
s over a finite alphabet\, one can measure the distance between them by lo
oking how their asymptotic behaviours differ. This gives rise to dynamical
ly generated Besicovitch pseudometric. I will talk about the generalisatio
n of this concept to actions of countable amenable groups. I will show tha
t it induces a metric on the space of ergodic measures invariant under the
action\, and that in the case of the shift space\, entropy function is co
ntinuous with respect to this metric. As an application of these results\,
I will show that if the considered group is in addition residually finite
\, then uniquely ergodic measures are entropy dense in the set of totally
ergodic measures. This is a joint work with Martha Łącka.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Boroński
DTSTART:20210122T091500Z
DTEND:20210122T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/20
DESCRIPTION:Title: Parametric families of attractors and inverse limits\nby Jan Bor
oński as part of Dynamical systems seminar at the Jagiellonian University
\n\nLecture held in 1016.\n\nAbstract\nIn my talk I shall discuss some of
my recent work on\nparametric families of maps and their strange attractor
s on surfaces\,\nwhich employed inverse limit approach. They were focusing
on computing\naccessible rotation numbers (e.g. for reduced Arnold Standa
rd Family\n[1])\, and building 1-dimensional models that are reductions of
\n2-dimensional dynamics in the presence of strong (mild) dissipation\n[2]
. The latter was inspired by recent results of Crovisier and Pujals\n[3] (
see also [4]).\n\nReferences\n[1] Boroński\, J. P.\; Činč\, J.\; Liu\,
X-C "Prime ends dynamics in\nparametrised families of rotational attractor
s". J. Lond. Math. Soc.\n(2) 102 (2020)\, no. 2\, 557–579.\n[2] Topologi
cal and Smooth Dynamics on Surfaces\, Mathematisches\nForschungsinstitut O
berwolfach Report No. 27/2020\, DOI:\n10.4171/OWR/2020/27\n[3] S. Crovisie
r\, E. Pujals\, "Strongly dissipative surface\ndiffeomorphisms"\, Commenta
rii Mathematici Helvetici 93 (2018)\,\n377–400.\n[4] S. Crovisier\, E. P
ujals\, C\, Tresser\, "Mild dissipative\ndiffeomorphisms of the disk with
zero entropy"\, arXiv 2020.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sascha Troscheit
DTSTART:20210305T091500Z
DTEND:20210305T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/21
DESCRIPTION:Title: A dimension theory approach to embeddings in random geometry\nby
Sascha Troscheit as part of Dynamical systems seminar at the Jagiellonian
University\n\nLecture held in 1016.\n\nAbstract\nThe continuum random tre
e and Brownian map are important\nmetric spaces in probability theory and
represent the "typical" tree\nand metric on the sphere\, respectively. The
Brownian map in particular\nis linked to Liouville Quantum Gravity but th
e exact nature of the\ncorrespondence is unknown.\nIn this talk I will exp
lain a fairly dynamical construction of these\nspaces and show how recent
advances in the dimension theory of\nself-similar sets can be used to shed
light on general embedding\nproblems. In particular\, I will show that th
e Assouad dimension of\nthese metric spaces is infinite and show how this
restricts the nature\nof embeddings. Time permitting\, I will also indicat
e how the\nconstruction of continuum trees may be used to analyse highly s
ingular\nfunctions such as the Weierstrass-type functions.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurelia Bartnicka
DTSTART:20210326T091500Z
DTEND:20210326T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/22
DESCRIPTION:Title: Topological dynamics of multidimensional $\\mathscr{B}$-free systems
: proximality\, minimality and maximal equicontinuous factor.\nby Aure
lia Bartnicka as part of Dynamical systems seminar at the Jagiellonian Uni
versity\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Barge
DTSTART:20210409T081500Z
DTEND:20210409T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/23
DESCRIPTION:by Hector Barge as part of Dynamical systems seminar at the Ja
giellonian University\n\nLecture held in 1016.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Konieczny
DTSTART:20210312T091500Z
DTEND:20210312T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/24
DESCRIPTION:Title: Quasicrystals from the point of view of additive combinatorics\n
by Jakub Konieczny as part of Dynamical systems seminar at the Jagiellonia
n University\n\nLecture held in 1016.\n\nAbstract\nWe show that some resul
ts in additive combinatorics can\nbe translated into corresponding results
that are relevant to the\nmathematical theory of quasicrystals. Specifica
lly\, we will use the\nFreiman–Ruzsa theorem\, characterising finite set
s with bounded\ndoubling\, to obtain an alternative proof of a characteris
ation of\nMeyer sets\, that is\, relatively dense subsets of Euclidean spa
ces\nwhose difference sets are uniformly discrete.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maik Gröger
DTSTART:20210319T091500Z
DTEND:20210319T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/25
DESCRIPTION:Title: Group actions with discrete spectrum and their amorphic complexity\nby Maik Gröger as part of Dynamical systems seminar at the Jagielloni
an University\n\nLecture held in 1016.\n\nAbstract\nAmorphic complexity\,
originally introduced for integer actions\, is a\ntopological invariant wh
ich measures the complexity of dynamical\nsystems in the regime of zero en
tropy.\nWe will explain its definition for actions by locally compact\nsig
ma-compact amenable groups on compact metric spaces.\nAfterwards\, we will
illustrate some of its basic properties and show\nwhy it is tailor-made t
o study strictly ergodic group actions with\ndiscrete spectrum and continu
ous eigenfunctions.\nThis class of actions includes\, in particular\, Delo
ne dynamical\nsystems related to regular model sets obtained via cut and p
roject\nschemes (CPS).\nFinally\, for this family of Delone dynamical syst
ems we present sharp\nupper bounds on amorphic complexity utilizing basic
properties of the\ncorresponding CPS.\nThis is joint work with G. Fuhrmann
\, T. Jäger and D. Kwietniak.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Raszeja (University of São Paulo (USP)\, Brazil)
DTSTART:20210428T131500Z
DTEND:20210428T144500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/26
DESCRIPTION:Title: Thermodynamic formalism on generalized countable Markov shifts\n
by Thiago Raszeja (University of São Paulo (USP)\, Brazil) as part of Dyn
amical systems seminar at the Jagiellonian University\n\nLecture held in 1
016.\n\nAbstract\nGiven a 0-1 infinite matrix $A$\, R. Exel and M. Laca ha
ve\nintroduced a kind of \\textit{generalized countable Markov shift}\n(GC
MS) $X_A=\\Sigma_A \\cup Y_A$\, which is a locally compact (in many\nimpor
tant cases compact) version of $\\Sigma_A$\, the standard countable\nMarko
v shift. The elements of $Y_A$ are finite words\, possibly\nincluding mult
iplicities. We develop the thermodynamic formalism for\nGCMS\, where we in
troduced the notion of conformal measure on $X_A$\,\nand we explored its c
onnections with the usual formalism on\n$\\Sigma_A$. Among the results\, w
e highlight the finding of new\nconformal measures that are not detected b
y the thermodynamic\nformalism on $\\Sigma_A$ and new phase transition phe
nomena: for a wide\nclass of GCMS and potentials\, we determined regions f
or the inverse of\nthe temperature $\\beta$\, where we absence\\existence
of these new\nconformal probabilities\, living on $Y_A$. The Gurevich entr
opy $h_G$\nplays a fundamental role in determining these regions since the
\ncritical value for gauge potentials is $h_G$ when finite. We also have\n
phase transition results for $h_G = \\infty$\, including the full shift.\n
In addition\, for the eigenmeasures of Ruelle's transformation\, we\ndisco
vered a length-type phase transition in the renewal shift: the\nexistence
of a critical value for $\\beta$ where the measure passes\nfrom living on
$\\Sigma_A$ to live on $Y_A$. We showed that the notion\nof pressure intro
duced by M. Denker and M. Yuri for Iterated Function\nSystems (IFS) is a n
atural definition of pressure for $X_A$\, and it\ncoincides with the Gurev
ich pressure for GCMS basically for the same\ngenerality on which the ther
modynamic formalism is developed for the\nstandard countable Markov shifts
and potentials.\n\nJoint work with R. Bissacot (University of São Paulo
(USP)\, Brazil)\,\nR. Exel (Federal University of Santa Catarina (UFSC)\,
Brazil)\, and R.\nFrausino (University of Wollongong (UOW)\, Australia).\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elżbieta Krawczyk (Jagiellonian University)
DTSTART:20210507T081500Z
DTEND:20210507T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/27
DESCRIPTION:Title: Automatic sequences in automatic systems\nby Elżbieta Krawczyk
(Jagiellonian University) as part of Dynamical systems seminar at the Jagi
ellonian University\n\nLecture held in 1016.\n\nAbstract\nA sequence is ca
lled automatic if it can be obtained as a coding of a fixed point of a sub
stitution of constant length. We study the class of automatic systems\, th
at is systems which arise as orbit closures of automatic sequences. \n\nSi
nce there are only countably many automatic sequences\, and since automati
c systems usually have uncountably many points\, it is interesting to stud
y the combinatorial structure of the subset of an automatic system which c
omprises all of its points which are automatic. We give a dynamical descri
ption of this set\, which is analogous to the one obtained by Holton and Z
amboni for minimal substitutive systems. In particular\, we show that auto
matic sequences in an infinite minimal automatic system correspond to the
rationals in the ring of k-adic integers\, the maximal connected equiconti
nuous factor of the system. \n\n As an application\, we show that any mini
mal substitutive system which factors onto an infinite k-automatic system
is itself k-automatic. We also state several conjectures which generalise
our results to arbitrary substitutive systems\, and explain their relation
to Cobham-type results (connected with the ones obtained by Durand in 201
1).\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Trilles (Jagiellonian University)
DTSTART:20210514T081500Z
DTEND:20210514T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/28
DESCRIPTION:Title: Topological stability of iterated function systems\nby Alexandre
Trilles (Jagiellonian University) as part of Dynamical systems seminar at
the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nWe stud
y Iterated Function Systems (IFS) with compact parameter space.\nWe show t
hat the compactness of the phase space permits us to obtain a natural metr
ic\non the space of IFS which extends $C^0$-topology to the space of IFS.\
nWe then use this metric to define topological stability and to prove that
\nin this context the classical results saying that shadowing property is
a necessary\ncondition for topological stability and that shadowing proper
ty together\nwith expansiveness are sufficient conditions.\n\nFor a proof
of these statements\, in fact we use a stronger type of shadowing property
\nwhich we show to be different than the standard one.\n\nThis is joint wo
rk with Alexander Arbieto.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Stadlbauer (Universidade Federal do Rio de Janeiro)
DTSTART:20210521T081500Z
DTEND:20210521T094500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/29
DESCRIPTION:Title: A logarithmic law for continued fractions with sequentially restrict
ed entries\nby Manuel Stadlbauer (Universidade Federal do Rio de Janei
ro) as part of Dynamical systems seminar at the Jagiellonian University\n\
n\nAbstract\nNon-stationary shift spaces are basic models of sequential dy
namical system who were intensively studied in order to construct symbolic
models for ergodic automorphism (Vershik) or in the context of the isomor
phism problem of shift spaces (Krieger). Recently\, the focus moved toward
s thermodynamic formalism and related questions. A fundamental tool of the
rmodynamic formalism\, Ruelle's operator theorem\, has no immediate genera
lization to the non-stationary setting as invariant functions intrinsicall
y may not exist. However\, it is possible to establish geometric ergodicit
y for a family of ratios of operators. \n\nThis approach has applications
to a classical problem in metric number theory. For a sequence $(\\alpha_n
)$ converging to $\\infty$\, set \n\\[X_\\alpha := \\left\\{ x = \\frac{1}
{x_1 + \\frac{1}{x_2 + \\cdots} } : x_n \\in \\mathbb N\, x_n \\geq \\al
pha_n \\hbox{ for all } n \\right\\}.\\] \nThat is\, $X$ is the subset of
$[0\,1]$ such that the $n$-th entry of the continued fraction expansion o
f each element is bigger than or equal to $\\alpha_n$. In this setting\, f
or $\\alpha_n \\gg n^{1+\\epsilon}$\, the geometric ergodicity implies a
law of the iterated logarithm for square integrable functions from geometr
ic ergodicity. If\, in addition\, $(\\alpha_n)$ does not behave too wildly
\, the reference measure is absolutely contiunous with respect to the Haus
dorff measure (and the Hausdorff dimension is $1/2$). \\\\\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Lemańczyk (University of Warsaw)
DTSTART:20211203T091500Z
DTEND:20211203T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/30
DESCRIPTION:Title: Topological pressure of convolution systems with application to B-fr
ee systems\nby Michał Lemańczyk (University of Warsaw) as part of Dy
namical systems seminar at the Jagiellonian University\n\nLecture held in
1016.\n\nAbstract\nI will introduce the notion of a convolution system and
show formulas\nfor the topological pressure in this setting. As an applic
ation\, I\nwill give a plain formula for the topological pressure for the\
nhereditary closure of any B-free system (for an arbitrary continuous\npot
ential). The talk will be based on joint paper with Joanna\nKułaga-Przymu
s.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Antoine Guihéneuf (Sorbonne Université)
DTSTART:20211210T091500Z
DTEND:20211210T104500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/31
DESCRIPTION:Title: Two examples of systems with historic behaviour\nby Pierre-Antoi
ne Guihéneuf (Sorbonne Université) as part of Dynamical systems seminar
at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nA sys
tem is said to have historic behaviour if there is a\npositive Lebesgue me
asure set of points having non convergent Birkhoff\naverages. The question
of knowing whether systems with historic\nbehaviour are abundant in some
families of dynamics has recently\nregained attention\, with the recent wo
rks of Kiriki and Soma\, and\nBerger's definition of (local) emergence\, w
hich measures how big is the\nset of accumulation points of Birkhoff avera
ges.\n\nIn this talk\, I will present two examples of systems with histori
c\nbehaviour.\n\nThe first one\, obtained with Guarino and Santiago\, is a
modification of\nBowen's eye example in which the set of points with hist
oric behaviour\nis of positive Lebesgue measure but nowhere dense.\n\nThe
second one\, in collaboration with Andersson\, is the study of\nreparametr
ized linear flows of the two torus with two fixed points\; we\nobtain some
Diophantine conditions on the flow's parameters under which\nthe system h
as/has not historic behaviour.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Kanigowski (University of Maryland)
DTSTART:20220311T151500Z
DTEND:20220311T164500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/32
DESCRIPTION:Title: Ergodic and statistical properties of smooth systems\nby Adam Ka
nigowski (University of Maryland) as part of Dynamical systems seminar at
the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nWe will
discuss some classical ergodic (Bernoulli\, K-property\, positive entropy.
..) and statistical (limit theorems\, quantitative mixing...) properties o
f smooth dynamical systems. We will discuss their flexibility (i.e. non-tr
ivial examples of systems which satisfy some but not all of them) and rigi
dity (i.e. some properties imply other). We will mostly focus on two resul
ts: 1) exponential mixing implies Bernoulli 2) existence of zero entropy
systems satisfying a central limit theorem.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sohail Farhangi (Ohio State University)
DTSTART:20220318T150000Z
DTEND:20220318T164500Z
DTSTAMP:20260404T111243Z
UID:DSSUJ/33
DESCRIPTION:Title: Enhancements of van der Corput's Difference Theorem and connections
to the ergodic hierarchy of mixing.\nby Sohail Farhangi (Ohio State Un
iversity) as part of Dynamical systems seminar at the Jagiellonian Univers
ity\n\nLecture held in 1016.\n\nAbstract\nWe will examine three commonly u
sed variants of van der\nCorput's Difference Theorem (vdCDT) in Hilbert sp
aces and show that\nthey are associated with the notions of weak mixing\,
strong mixing\,\nand Bernoullicity. We will then use this association to d
erive 2 new\nvdCDTs corresponding to ergodicity and mild mixing. We remar
k that\nour methods naturally yield vdCDTs for a class of unbounded sequen
ces\nof vectors. We will then obtain an application to recurrence in\nmeas
ure preserving systems by giving a partial answer to a question of\nFrantz
ikinakis. If time permits\, we will also discuss analogues of\nthese vdCDT
s in the context of uniform distribution and the classes of\n"mixing distr
ibutions" that they produce.\n
LOCATION:https://stable.researchseminars.org/talk/DSSUJ/33/
END:VEVENT
END:VCALENDAR