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Webinar in dynamical systems:
Eduardo Garibaldi (UNICAMP)
Philippe Thieullen (Bordeaux)
(Thermodynamic formalism,
ergodic optimization,
Gibbs measures,
low complexity,
random dynamical systems)
Every two weeks
Brazilian time: 10:30-11h30, French time: 15h30-16h30
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Last update
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June 17th 2025
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Forthcoming speakers
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2025/06/17:
Samuel Petite (Amiens)
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Title: Language stable shifts
Abstract: language stable shifts form a rich class of shifts that was recently
introduced by V. Cyr and B. Kra. This family contains many classical examples of
subshifts, of various complexities ranging from systems of strictly positive
entropy, such as subshift finite-type (SFT), to systems of low complexity, such
as shifts of linear complexity. They are generic among the family of shifts. In
this talk, we present some of their properties, in particular those concerning the
cellular automata preserving them and their invariant measures
Cleber Fernando Colle (UFABC)
Title: Nonexpansive subspaces and Nivat's conjecture
Abstract: In his Ph.D. thesis, Michal Szabados showed that every configuration
with low pattern complexity can be decomposed into a finite sum of periodic
configurations. In this webinar, I will present some results and open problems
related to nonexpansive subspaces, periodic decompositions, and Nivat's
conjecture - a natural generalization of the Morse–Hedlund theorem to the
two-dimensional case.
Past speakers
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2025/06/03: Sandro Vaienti (Marseille)
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ZOOM
Title: Quasi limit theorems for open systems
Abstract: We investigate deterministic and random open dynamical systems (with holes),
and we give limit theorems characterizing the converge to the equilibrium state on the
surviving set
Ali Messaoudi (UNESP)
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ZOOMTitle: Substitution dynamical systems on infinite alphabets
Abstract: A substitution is a map from an alphabet A to the set of finite words
in A. To any substitution we can naturally associate a symbolic dynamical system
that is well studied in the literature when the alphabet is a finite set and
connected to several areas such as ergodic theory and number theory among others.
In this work, we study ergodic and geometric properties of dynamical systems
associated to substitutions in infinite alphabets. This study involves finite
and infinite invariant measures, countably infinite matrices and Rauzy Fractals.
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2025/05/20:
Mathieu Sablik (Toulouse)
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ZOOM
Title: Characterization of zero-noise limit measures for cellular automata
Abstract: For a given cellular automaton F , define $F_\epsilon$ its perturbation by
a noise of size $\epsilon$
and denote by $\pi_\epsilon$ one of its invariant measure. The zero-noise limit measures are
the accumulation points of $\pi_\epsilon$ as $\epsilon$ goes to 0. Zero-noise limit measure
represent invariant measures
``with a physical meaning'' because they appear even with a little noise.
We will illustrate this notion with some examples and look at which set can be realized as the set of zero-noise limit measures of a CA.
Marcelo Sobottka (UFSC)
PDF
ZOOM
Title: Blur Shifts
Abstract: Shift spaces are dynamical systems usually considered in symbolic dynamics.
Given a nonempty set of symbols $A$ (alphabet), the full shift is defined as the space
of all sequences over the alphabet $A$,
$$A^\mathbb{N}:=\{(x_i)_{i\in\mathbb{N}}:\ x_i\in A\ \forall i\in\mathbb{N}\}.$$
In $A^\mathbb{N}$, we consider the prodiscrete topology and the shift map
$\sigma:A^\mathbb{N}\to A^\mathbb{N}$ given by
$$\sigma\big((x_i)_{i\in\mathbb{N}}\big)=(x_{i+1})_{i\in\mathbb{N}}.$$
A shift space is any subspace $\Lambda\subset A^\mathbb{N}$ that is closed in
$A^\mathbb{N}$ and such that $\sigma(\Lambda)\subset\Lambda$.
When $A$ is a finite set, shift spaces are compact, and there is an extensive
theory about them. On the other hand, if $A$ is infinite, the loss of compactness
(and often even of local compactness) introduces several challenges to their study.
In this webinar I will present a new type of shift spaces, called blur shifts, that
were proposed in a joint work with Tadeu Zavistanovicz de Almeida. These spaces are
constructed from classical shift spaces by selecting certain infinite sets of symbols
to be represented by a new symbol and then defining a suitable topology. In particular,
blur shifts can be used as a compactification scheme for classical shift spaces.
Finally, we present some examples of applications of blur shifts.
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2025/05/06:
Eduardo Garibaldi (UNICAMP)
Title: Equilibrium states and statistical properties for intermittent maps
Léo Gayral (Nancy)
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Title: Robustness to Perturbations of the Gibbs Potential:
Philippe Thieullen (Bordeaux)
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Title: Genericity in ergodic optimization
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