Seminario de Sistemas Dinámicos
El Seminario de Sistemas Dinámicos de Santiago es el encuentro semanal de matemáticas con mayor tradición en el país pues se realiza ininterrumpidamente desde la década del '80. Se realiza alternadamente en alguna de las instituciones de Santiago donde hay miembros del grupo de Sistemas Dinámicos. Participan así las universidades de Chile, de Santiago, Andrés Bello y Católica de Chile.
2026-09-28
16:30hrs.
16:30hrs.
Xavier Jarque. Universitat de Barcelona
The Escaping Set
Sala 1
Abstract:
The Escaping Set
Sala 1
Abstract:
The escaping set of a transcendental entire function consists of the points whose iterates tend to infinity. This talk is a survey of the main results on the escaping set over the past twenty years, including the author's own contributions to the subject.
2026-09-21
16:30hrs.
16:30hrs.
Marisa Cantarino. Universidad de Chile
Towards rigorous bounds on Lyapunov exponents for Anosov diffeomorphisms
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
The rigorous computation of Lyapunov exponents for smooth dynamical systems involves the computation of lower and upper bounds for their values. Applying techniques from the seminal work of Baladi and Tsujii on anisotropic Banach spaces for uniformly hyperbolic dynamics, we can prove upper and lower bounds for Lyapunov exponents in terms of the spectral radii of transfer operators.
Towards rigorous bounds on Lyapunov exponents for Anosov diffeomorphisms
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
Lyapunov exponents express the exponential growth rate of distances in the system and provide a quantitative value associated with the complexity of the system, being related as well to the entropy.
The rigorous computation of Lyapunov exponents for smooth dynamical systems involves the computation of lower and upper bounds for their values. Applying techniques from the seminal work of Baladi and Tsujii on anisotropic Banach spaces for uniformly hyperbolic dynamics, we can prove upper and lower bounds for Lyapunov exponents in terms of the spectral radii of transfer operators.
We illustrate the implementation of a converging numerical scheme to compute these spectral radii, and discuss how we can make most of the steps of this computation rigorous.
This presentation is based on ongoing work joint with Bastián Núñez-Boettiger, Ekaterina Shchetka, and Truong Vu.
2026-09-07
16:30hrs.
16:30hrs.
Sam Corson. Universidad Politécnica de Madrid
Large Artinian Groups
Sala de Seminarios Maryam Mirzakhani, Departamento de Matemáticas, Facultad de Ciencias (Campus Juan Gómez Millas), Universidad de Chile
Abstract:
I will review some classical examples of groups whose strictly descending chains of subgroups are finite. Some recent constructions of such groups (having large cardinality) will also be explained. Set-theoretic consistency will play a role in some of the stated results. This is joint work with Saharon Shelah.
Large Artinian Groups
Sala de Seminarios Maryam Mirzakhani, Departamento de Matemáticas, Facultad de Ciencias (Campus Juan Gómez Millas), Universidad de Chile
Abstract:
I will review some classical examples of groups whose strictly descending chains of subgroups are finite. Some recent constructions of such groups (having large cardinality) will also be explained. Set-theoretic consistency will play a role in some of the stated results. This is joint work with Saharon Shelah.
2026-08-24
16:30hrs.
16:30hrs.
Mike Todd. University of St Andrews
Equidistribution in dynamical systems
Sala 1
Abstract:
Given an ergodic dynamical system, the proportion of times a typical orbit spends in a given set is asymptotically the measure of that set. We can quantify how close an orbit is to this equidistribution by taking $\delta>0$ and $\epsilon>0$ and seeing how long it takes for the orbit to have hit every $\delta$-ball a proportion of the time greater than $(1-\epsilon)$ times the measure of that ball. Computing the expected value of such a `blanket time' is a classical problem in probability, particularly for random walks on finite graphs. Here we give asymptotics for the expectation for small $\delta, \epsilon$, a type of quantitative equidistribution, for a class of dynamical systems. This is joint work with Natalia Jurga.
Equidistribution in dynamical systems
Sala 1
Abstract:
Given an ergodic dynamical system, the proportion of times a typical orbit spends in a given set is asymptotically the measure of that set. We can quantify how close an orbit is to this equidistribution by taking $\delta>0$ and $\epsilon>0$ and seeing how long it takes for the orbit to have hit every $\delta$-ball a proportion of the time greater than $(1-\epsilon)$ times the measure of that ball. Computing the expected value of such a `blanket time' is a classical problem in probability, particularly for random walks on finite graphs. Here we give asymptotics for the expectation for small $\delta, \epsilon$, a type of quantitative equidistribution, for a class of dynamical systems. This is joint work with Natalia Jurga.
2026-08-17
16:30hrs.
16:30hrs.
Till Hauser. Pontificia Universidad Católica
Mean Equicontinuity and Related Properties in Hyperspace and Measure Dynamics
Sala 1
Abstract:
Motivated by applications in statistical physics, we study the induced dynamical systems $(\mathcal{M}(X),T)$ and $(\mathcal{H}(X),T)$, consisting respectively of Borel probability measures and non-empty closed subsets of a dynamical system $(X,T)$. In this talk, we first survey the inheritance of various well-studied dynamical properties, including equicontinuity, distality, pointwise almost periodicity, transitivity, weak mixing, nullness, tameness, and zero entropy. We then turn to mean equicontinuity, diam-mean equicontinuity, and weak-mean equicontinuity, and discuss new inheritance results with respect to these notions. These results complete the picture and reveal another interesting asymmetry between the hyperspace and measure-theoretic constructions. The talk focuses on continuous surjective maps $T\colon X\to X$, while the new results can also be extended to actions of locally compact $\sigma$-compact amenable groups.
This is a joint work with Chunlin Liu and María Isabel Cortez.
Mean Equicontinuity and Related Properties in Hyperspace and Measure Dynamics
Sala 1
Abstract:
Motivated by applications in statistical physics, we study the induced dynamical systems $(\mathcal{M}(X),T)$ and $(\mathcal{H}(X),T)$, consisting respectively of Borel probability measures and non-empty closed subsets of a dynamical system $(X,T)$. In this talk, we first survey the inheritance of various well-studied dynamical properties, including equicontinuity, distality, pointwise almost periodicity, transitivity, weak mixing, nullness, tameness, and zero entropy. We then turn to mean equicontinuity, diam-mean equicontinuity, and weak-mean equicontinuity, and discuss new inheritance results with respect to these notions. These results complete the picture and reveal another interesting asymmetry between the hyperspace and measure-theoretic constructions. The talk focuses on continuous surjective maps $T\colon X\to X$, while the new results can also be extended to actions of locally compact $\sigma$-compact amenable groups.
This is a joint work with Chunlin Liu and María Isabel Cortez.
2026-08-10
16:30hrs.
16:30hrs.
Sebastián Muñoz Thon. Université Paris-Saclay
Decay of correlations on Abelian covers of isometric extensions of Anosov flows.
Auditorio Ninoslav Bralic
Abstract:
Decay of correlations on Abelian covers of isometric extensions of Anosov flows.
Auditorio Ninoslav Bralic
Abstract:
I will report on a recent work with M. Ceki? and T. Lefeuvre. We prove a complete asymptotic expansion of the correlation function in inverse powers of the time variable, for flows which arise as Abelian extensions, that is, extensions to $\mathbb{Z}^d$-covers, of certain partially hyperbolic flows. This includes the frame flow of an Abelian cover of a negatively curved closed Riemannian manifold $(M, g)$, if the frame flow on $(M, g)$ is ergodic. As a special case, our theorem also applies to Abelian extensions of Anosov flows. The proof uses Fourier series in $\mathbb{Z}^d$ (Floquet theory), (microlocal) anisotropic Sobolev spaces tailored to the dynamics, as well as the semiclassical Borel-Weil calculus on principal bundles.
2026-07-27
16:30hrs.
16:30hrs.
Guillaume Theyssier. Cnrs / Aix-Marseille Université
Stabilization of subshifts of finite type by cellular automata
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
A subshift of finite type (SFT) is a set of infinite (d-dimensional) configurations defined by a finite set of local constraints (e.g. the set of 3-coloring of the grid). N. Fatès, I. Marcovici et S. Taati introduced in 2021 the following notion of stabilization: an SFT Σ is stabilizable if there is a cellular automaton F which
1) leave invariant any configuration of Σ, and
2) starting from any finite perturbation of any configuration of Σ, F reaches in finite time a configuration from Σ.
The goal of this talk is to show that any SFT (in any dimension) is stabilizable, which was an open question of Fatès-Marcovici-Taati-2021. We will also show that, in dimension 1, the stabilization can always be achieved in linear time, which has consequences on the possibility to stabilize configurations under random perturbations.
Stabilization of subshifts of finite type by cellular automata
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
A subshift of finite type (SFT) is a set of infinite (d-dimensional) configurations defined by a finite set of local constraints (e.g. the set of 3-coloring of the grid). N. Fatès, I. Marcovici et S. Taati introduced in 2021 the following notion of stabilization: an SFT Σ is stabilizable if there is a cellular automaton F which
1) leave invariant any configuration of Σ, and
2) starting from any finite perturbation of any configuration of Σ, F reaches in finite time a configuration from Σ.
The goal of this talk is to show that any SFT (in any dimension) is stabilizable, which was an open question of Fatès-Marcovici-Taati-2021. We will also show that, in dimension 1, the stabilization can always be achieved in linear time, which has consequences on the possibility to stabilize configurations under random perturbations.
2026-07-20
16:30hrs.
16:30hrs.
Álvaro Bustos Gajardo. Universidad de Chile
El teorema de Cobham en los enteros Gaussianos
Sala de Seminarios Maryam Mirzakhani, Departamento de Matemáticas, Facultad de Ciencias (campus Juan Gómez Millas), Universidad de Chile
Abstract:
Un conjunto de números naturales A se dice b-automático si es posible determinar si un número n pertenece a A examinando su expansión en base b mediante un autómata finito (un tipo muy sencillo de "computador"). Uno de los teoremas centrales de la teoría de conjuntos automáticos es el teorema de Cobham, el cual señala que un conjunto que es automático en varias bases independientes necesariamente es muy parecido a una progresión aritmética (es "casi periódico"). Este teorema ha sido generalizado en una gran variedad de contextos, incluyendo el punto de vista lógico y el de los sistemas dinámicos.
Entre estas posibles vias de generalización, se ha dedicado mucho trabajo a la búsqueda de teoremas análogos en otros (semi-)anillos que admiten sistemas de numeración. Intentos previos de encontrar este tipo de generalizaciones comenzaban desde la hipótesis de que este tipo de teoremas requerían un conocimiento fuerte de la estructura del anillo subyacente, y por ende dependían de conjeturas profundas aún no resueltas de teoría de números. Basándonos en una demostración alternativa del teorema original propuesta por Thijmen Krebs, en esta charla discutiremos una generalización completa del teorema de Cobham al anillo Z[i] de los enteros Gaussianos, la cual se basa en argumentos relativamente elementales. Esto sugiere que dichas consideraciones de teoría de números podrían no ser necesarias en general. Este trabajo ha sido realizado en conjunto con Reem Yassawi y Robbert Fokkink.
El teorema de Cobham en los enteros Gaussianos
Sala de Seminarios Maryam Mirzakhani, Departamento de Matemáticas, Facultad de Ciencias (campus Juan Gómez Millas), Universidad de Chile
Abstract:
Un conjunto de números naturales A se dice b-automático si es posible determinar si un número n pertenece a A examinando su expansión en base b mediante un autómata finito (un tipo muy sencillo de "computador"). Uno de los teoremas centrales de la teoría de conjuntos automáticos es el teorema de Cobham, el cual señala que un conjunto que es automático en varias bases independientes necesariamente es muy parecido a una progresión aritmética (es "casi periódico"). Este teorema ha sido generalizado en una gran variedad de contextos, incluyendo el punto de vista lógico y el de los sistemas dinámicos.
Entre estas posibles vias de generalización, se ha dedicado mucho trabajo a la búsqueda de teoremas análogos en otros (semi-)anillos que admiten sistemas de numeración. Intentos previos de encontrar este tipo de generalizaciones comenzaban desde la hipótesis de que este tipo de teoremas requerían un conocimiento fuerte de la estructura del anillo subyacente, y por ende dependían de conjeturas profundas aún no resueltas de teoría de números. Basándonos en una demostración alternativa del teorema original propuesta por Thijmen Krebs, en esta charla discutiremos una generalización completa del teorema de Cobham al anillo Z[i] de los enteros Gaussianos, la cual se basa en argumentos relativamente elementales. Esto sugiere que dichas consideraciones de teoría de números podrían no ser necesarias en general. Este trabajo ha sido realizado en conjunto con Reem Yassawi y Robbert Fokkink.
2026-06-22
16:30hrs.
16:30hrs.
Miguel Donoso-Echenique. Universität Münster
Existencia y (no-)unicidad de extensiones invertibles de acciones de semigrupos
Sala 2
Abstract:
La extensión natural es una construcción clásica en teoría ergódica que asocia a cada sistema no-invertible un sistema invertible que lo extiende. En esta charla formalizaremos la noción de extensión invertible para el caso general de acciones de semigrupos que preservan una medida de probabilidad. Luego estudiaremos el problema de la existencia de extensiones invertibles, y analizaremos casos en los que se tiene y no se tiene unicidad de éstas.
Existencia y (no-)unicidad de extensiones invertibles de acciones de semigrupos
Sala 2
Abstract:
La extensión natural es una construcción clásica en teoría ergódica que asocia a cada sistema no-invertible un sistema invertible que lo extiende. En esta charla formalizaremos la noción de extensión invertible para el caso general de acciones de semigrupos que preservan una medida de probabilidad. Luego estudiaremos el problema de la existencia de extensiones invertibles, y analizaremos casos en los que se tiene y no se tiene unicidad de éstas.
2026-06-15
16:30hrs.
16:30hrs.
Juan Peña. Universidad de Chile
Expansividad de sistemas no invertibles
Sala 1 (Albert Einstein), Departamento de Física, Facultad de Ciencias (Campus Juan Gómez Millas), Universidad de Chile
Abstract:
Recordatorio: Esta charla se realizará en el Campus Juan Gómez Millas de la Universidad de Chile.
Los flujos y homeomorfismos expansivos en espacios métricos compactos han sido extensamente estudiados debido a sus propiedades ergódicas. Recientemente, se ha trabajado en extender estos resultados a sistemas no invertibles, esto es, endomorfismos y semiflujos.
En esta charla contrastaremos dos formas que han surgido para abordar este problema, la expansividad positiva y los límites inversos. Repasaremos los resultados de Jaque y Herrero, que muestran ciertas limitaciones impuestas por la propiedad de expansividad positiva. Tras esto, veremos como los límites inversos nos permiten trabajar con un mayor conjunto de sistemas dinámicos y construiremos ejemplos no triviales de sistemas no invertibles con propiedades expansivas.
Expansividad de sistemas no invertibles
Sala 1 (Albert Einstein), Departamento de Física, Facultad de Ciencias (Campus Juan Gómez Millas), Universidad de Chile
Abstract:
Recordatorio: Esta charla se realizará en el Campus Juan Gómez Millas de la Universidad de Chile.
Los flujos y homeomorfismos expansivos en espacios métricos compactos han sido extensamente estudiados debido a sus propiedades ergódicas. Recientemente, se ha trabajado en extender estos resultados a sistemas no invertibles, esto es, endomorfismos y semiflujos.
En esta charla contrastaremos dos formas que han surgido para abordar este problema, la expansividad positiva y los límites inversos. Repasaremos los resultados de Jaque y Herrero, que muestran ciertas limitaciones impuestas por la propiedad de expansividad positiva. Tras esto, veremos como los límites inversos nos permiten trabajar con un mayor conjunto de sistemas dinámicos y construiremos ejemplos no triviales de sistemas no invertibles con propiedades expansivas.
2026-05-25
16:30hrs.
16:30hrs.
Bill Mance. Adam Mickiewicz University
Independence of notions from dynamics: a descriptive set theoretic approach
Sala 2
Abstract:
Independence of notions from dynamics: a descriptive set theoretic approach
Sala 2
Abstract:
As a special case of a theorem of Pollington, the set of numbers that are normal in base $2$, but not normal in base $3$ is known to have full Hausdorff dimension. An interpretation of results such as this are that in some way the notions of normality in base $2$ and normality in base $3$ are "independent".
The purpose of this talk is to introduce notions from descriptive set theory that may better capture this idea of independence: that of $D_2(\Sigma^0_\alpha)$- and $D_2(\Pi^0_\alpha)$-completeness. For example, the previously mentioned set of numbers normal in base $2$, but not normal in base $3$ is known to be $D_2(\Pi^0_\alpha)$-complete by a recent result of Jackson, M., and Vandehey. Difference sets that satisfy these properties will also have additional interesting properties that will be discussed.
2026-05-25
17:30hrs.
17:30hrs.
Dominik Kwietniak. Jagiellonian University
Generic invariant measures beyond specification
Sala 2
Abstract:
Which properties hold for a generic invariant measure of a continuous map $T$ from a compact metric space $X$ to itself? We prove the genericity of rank one measures under a relaxed specification hypothesis (the vague specification or the approximate product property), sharpening Sigmund's classical genericity theorem. The method applies, in particular, to certain minimal and proximal systems. As a by-product, every measure produced by the Gorodetski–Ilyashenko–Kleptsyn–Nalsky construction of non-uniformly hyperbolic ergodic invariant measures is rank one.
The key new tools are an approximation scheme for the natural extension of T, inspired by the classical approximation of a subshift by a descending sequence of shifts of finite type, and notions of convergence of invariant measures generalising Ornstein's $d$-bar metric and Feldman's $f$-bar metric. Outside the symbolic setting, these notions of convergence are new and allow several classical results from the theory of $d$-bar and $f$-bar to be transferred to general topological dynamical systems.
Based on joint work with M. E. Can, J. Konieczny, M. Kupsa; with D. Buldag and B. Jacelon; and with M. Lacka and A. Trilles.
(Nota: algunos caracteres tuvieron que ser reemplazados por aproximaciones, por razones de compatibilidad)
Generic invariant measures beyond specification
Sala 2
Abstract:
Which properties hold for a generic invariant measure of a continuous map $T$ from a compact metric space $X$ to itself? We prove the genericity of rank one measures under a relaxed specification hypothesis (the vague specification or the approximate product property), sharpening Sigmund's classical genericity theorem. The method applies, in particular, to certain minimal and proximal systems. As a by-product, every measure produced by the Gorodetski–Ilyashenko–Kleptsyn–Nalsky construction of non-uniformly hyperbolic ergodic invariant measures is rank one.
The key new tools are an approximation scheme for the natural extension of T, inspired by the classical approximation of a subshift by a descending sequence of shifts of finite type, and notions of convergence of invariant measures generalising Ornstein's $d$-bar metric and Feldman's $f$-bar metric. Outside the symbolic setting, these notions of convergence are new and allow several classical results from the theory of $d$-bar and $f$-bar to be transferred to general topological dynamical systems.
Based on joint work with M. E. Can, J. Konieczny, M. Kupsa; with D. Buldag and B. Jacelon; and with M. Lacka and A. Trilles.
(Nota: algunos caracteres tuvieron que ser reemplazados por aproximaciones, por razones de compatibilidad)
2026-05-11
16:30hrs.
16:30hrs.
Diego Céspedes. Universidad de Chile
On the Divergence of Arithmetic Ergodic Averages
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
One of the central questions in ergodic theory is classifying which ergodic averages satisfy Birkhoff’s theorem. In this talk, we study a class of averages that do not necessarily arise from subsequences of integers. We prove a sufficient condition of Gaussian type, in the spirit of the Erd?s-Kac theorem, for the strong failure of their pointwise convergence. As an application, we answer a question posed by Donoso, Le, Moreira, and Sun. This is joint work with Sebastián Donoso.
On the Divergence of Arithmetic Ergodic Averages
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
One of the central questions in ergodic theory is classifying which ergodic averages satisfy Birkhoff’s theorem. In this talk, we study a class of averages that do not necessarily arise from subsequences of integers. We prove a sufficient condition of Gaussian type, in the spirit of the Erd?s-Kac theorem, for the strong failure of their pointwise convergence. As an application, we answer a question posed by Donoso, Le, Moreira, and Sun. This is joint work with Sebastián Donoso.
2026-04-27
16:30hrs.
16:30hrs.
Christopher Cabezas. Universidad de Chile
Notions of openness in semigroup actions
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
We study the notion of openness of shifts transformations given by abstract semigroup actions. In 1966, Parry proved that the only one-sided subshifts with open shift map are the SFTs. In our work, we extend this theorem in several directions for some abstract semigroup actions, introducing the notion of synchronizing sets and study some applications. We will also discuss some interesting examples on N2, Q+ and free semigroups. This is a joint work with Sebastian Donoso and Mattheiu Sablik.
Notions of openness in semigroup actions
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
We study the notion of openness of shifts transformations given by abstract semigroup actions. In 1966, Parry proved that the only one-sided subshifts with open shift map are the SFTs. In our work, we extend this theorem in several directions for some abstract semigroup actions, introducing the notion of synchronizing sets and study some applications. We will also discuss some interesting examples on N2, Q+ and free semigroups. This is a joint work with Sebastian Donoso and Mattheiu Sablik.
2026-04-13
16:30hrs.
16:30hrs.
Victor Janeiro. Universidade Federal de Minas Gerais
Medidas SRB para sistemas con expansión no uniforme
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
En este seminario presentaremos los resultados recientes de D. Burguet, así como de J. Buzzi, S. Crovisier y O. Sarig, sobre la existencia de medidas SRB (en particular, físicas) para difeomorfismos con expansión no uniforme en superficies. A continuación, estudiaremos ejemplos de endomorfismos no invertibles para los cuales podemos aplicar sus métodos y obtener medidas SRB inversas; dichos ejemplos están basados en el trabajo reciente de M. Andersson, P. Carrasco y R. Saghin. Las medidas SRB inversas, aunque poseen buenas propiedades ergódicas, se comportan de manera fuertemente distinta al caso invertible, como detallaremos. Este es un trabajo conjunto con Radu Saghin.
Medidas SRB para sistemas con expansión no uniforme
Sala de Seminarios (7° Piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
En este seminario presentaremos los resultados recientes de D. Burguet, así como de J. Buzzi, S. Crovisier y O. Sarig, sobre la existencia de medidas SRB (en particular, físicas) para difeomorfismos con expansión no uniforme en superficies. A continuación, estudiaremos ejemplos de endomorfismos no invertibles para los cuales podemos aplicar sus métodos y obtener medidas SRB inversas; dichos ejemplos están basados en el trabajo reciente de M. Andersson, P. Carrasco y R. Saghin. Las medidas SRB inversas, aunque poseen buenas propiedades ergódicas, se comportan de manera fuertemente distinta al caso invertible, como detallaremos. Este es un trabajo conjunto con Radu Saghin.
2026-03-30
16:30hrs.
16:30hrs.
Franco Gómez. Universidad de Chile
Acciones por difeomorfismos de clase C^1 de los grupos Baumslag-Solitar en compactos son afines
Sala 2 (Sala Compartida de Matemática y Física), Departamento de Matemáticas, Campus Juan Gómez Millas, Universidad de Chile
Abstract:
Acciones por difeomorfismos de clase C^1 de los grupos Baumslag-Solitar en compactos son afines
Sala 2 (Sala Compartida de Matemática y Física), Departamento de Matemáticas, Campus Juan Gómez Millas, Universidad de Chile
Abstract:
Los grupos Baumslag-Solitar ${\rm BS}(m,n)$ generan un interés dado la variedad en sus propiedades algebraicas y su comportamiento dinámico. De hecho, C. Bonatti, A. Navas, I. Monteverde y C. Rivas mostraron que ciertos grupos solubles (entre ellos ${\rm BS}(1,n)$) solamente pueden actuar de manera afín en $[0,1]$ cuando es por difeomorfismos de clase $\mathcal{C}^1$.
El motivo de esta charla es revisitar resultados de la dinamica 1-dimensional en acciones de grupos ${\rm BS}(m,n)$ y probar que en intervalos compactos las acciones por difeomorfismos de los grupos ${\rm BS}(m,n)$ (que no están incluidos en el trabajo de BMNR) son conjugadas a una acción estándar afín.
2026-03-23
16:30hrs.
16:30hrs.
Sebastián Donoso. Universidad de Chile
Partition Regularity for Quadratic Equations in Number Fields
Sala de Seminarios (7° piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
An equation is partition regular over its domain if, for any finite coloring of that domain, there exists a monochromatic nontrivial solution. In this talk, we will review the background of this topic, focusing on the ergodic theoretic tools used to tackle such problems and present a recent joint work with A. Koutsogiannis, A. Ferré Moragues and W. Sun, concerning the partition regularity problem of quadratic equations over some number fields.
Partition Regularity for Quadratic Equations in Number Fields
Sala de Seminarios (7° piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
An equation is partition regular over its domain if, for any finite coloring of that domain, there exists a monochromatic nontrivial solution. In this talk, we will review the background of this topic, focusing on the ergodic theoretic tools used to tackle such problems and present a recent joint work with A. Koutsogiannis, A. Ferré Moragues and W. Sun, concerning the partition regularity problem of quadratic equations over some number fields.
2026-01-19
16:30hrs.
16:30hrs.
Mélodie Andrieu. University of The Littoral Opal Coast
A Normality Conjecture on Rational Base Number Systems
Sala de Seminarios (7° piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
A Normality Conjecture on Rational Base Number Systems
Sala de Seminarios (7° piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two interesting families of infinite words emerge, called minimal and maximal words.
We formulate the conjecture that every minimal and maximal word is normal over an appropriate subalphabet.
The aim of the talk is to convince the audience that the conjecture seems true and of considerable difficulty. In particular, we shall discuss its connections with several older conjectures, including the existence of Z-numbers (Mahler, 1968) and Z_p/q-numbers (Flatto, 1992), the existence of triple expansions in rational base p/q (Akiyama, 2008), and the Collatz-inspired '4/3 problem' (Dubickas and Mossinghoff, 2009).
The talk is based on a joint work with Shalom Eliahou and Léo Vivion.
2026-01-12
16:30hrs.
16:30hrs.
Nicolò Paviato. Weizmann Institute of Science
Thresholds for Poisson Limits in Symbolic Dynamics
Sala 1 del Edificio Rolando Chuaqui
Abstract:
Thresholds for Poisson Limits in Symbolic Dynamics
Sala 1 del Edificio Rolando Chuaqui
Abstract:
About twenty years ago, Peres and Weiss generalised the classical Poisson limit theorem for appearances of words of increasing length in a sequence x. They showed that the theorem holds for almost every x with respect to the infinite uniform product measure. A natural question is whether this Poisson behaviour persists when the sequence is sampled according to a different product measure.
In our first result, we consider non-stationary product measures and show that there exists a quantitative threshold above which the Poisson limit theorem holds for almost every x, while below this threshold it may fail. In contrast, our second result shows that for a biased infinite product measure (a non-fair coin) the limiting behaviour is almost surely non-Poisson. This shows that the Poisson regime is specific to the equiprobable case and to small deviations from it.
This talk is based on works with Mike Hochman and Jon V. Kogan.
2026-01-07
14:00 hrs hrs.
14:00 hrs hrs.
Felipe Riquelme. Pontificia Universidad Católica de Valparaíso
Órbitas geodésicas y puntos límites
Sala 3
Abstract:
El objetivo de esta charla es explorar la relación entre la dinámica de las órbitas geodésicas en superficies hiperbólicas y la estructura de los puntos límite en el borde al infinito. En particular, presentaremos una demostración alternativa de un teorema de C. Bishop, que caracteriza la dimensión del conjunto límite en términos de los puntos límite radiales y de escape lineal. La principal ventaja de este enfoque es que permite extender el resultado a variedades de curvatura negativa de dimensión arbitraria. Este trabajo es en colaboración con D. Pizarro y S. Villarroel.
Órbitas geodésicas y puntos límites
Sala 3
Abstract:
El objetivo de esta charla es explorar la relación entre la dinámica de las órbitas geodésicas en superficies hiperbólicas y la estructura de los puntos límite en el borde al infinito. En particular, presentaremos una demostración alternativa de un teorema de C. Bishop, que caracteriza la dimensión del conjunto límite en términos de los puntos límite radiales y de escape lineal. La principal ventaja de este enfoque es que permite extender el resultado a variedades de curvatura negativa de dimensión arbitraria. Este trabajo es en colaboración con D. Pizarro y S. Villarroel.
Contáctenos
Edificio Rolando Chuaqui, Campus San Joaquín. Avda. Vicuña Mackenna 4860, Macul, Chile.Teléfono (+56) 95504 4511.
Formulario de Contacto