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.

 

2020-09-16
15:30hrs.
Jonathan Conejeros. Universidad de Santiago de Chile
Elementos de Distorsión en el Grupo de Difeomorfismos de la Esfera
Zoom (pedir link a Raimundo Briceño)
2020-09-09
15:30hrs.
Felipe García-Ramos. Universidad Autónoma de San Luis Potosí
Modelos Topológicos de Sistemas Loosely Bernoulli Con Entropía Cero
Zoom (pedir link a Raimundo Briceño)
2020-09-02
15:30hrs.
Godofredo Iommi. Pontificia Universidad Católica de Chile
Dimension Theory for Continued Fractions
Zoom (pedir link a Raimundo Briceño)
2020-08-26
15:30hrs.
Radu Saghin. Pontificia Universidad Católica de Valparaíso
Derivadas de Valores Propios y Exponentes de Lyapunov
Zoom (pedir link a Raimundo Briceño)
2020-08-19
15:45hrs.
Felipe Riquelme. Pontificia Universidad Católica de Valparaíso
Intermediate Entropy Property: old and New
Zoom (pedir link a Raimundo Briceño)
2020-07-13
16:30hrs.
Raimundo Briceño. Pontificia Universidad Católica de Chile
Kieffer-Pinsker Type Formulas for Gibbs Measures
Zoom (pedir link a Raimundo Briceño)
2020-07-06
16:30hrs.
Cristóbal Rivas. Universidad de Santiago de Chile
Acciones de Grupos Localmente Desplazantes
Zoom (pedir link a Raimundo Briceño)
2020-06-22
16:30hrs.
olga Lukina. University of Vienna
Stabilizers in Group Cantor Actions and Measures
Zoom (pedir link a Raimundo Briceño)
2020-06-15
16:30hrs.
Sebastián Barbieri. Labri, Université de Bordeaux
on The Relation Between Topological Entropy and Asymptotic Pairs
Zoom (pedir link a Raimundo Briceño)
2020-06-08
16:30hrs.
Andrés Navas. Universidad de Santiago de Chile
Distorted Diffeomorphisms and Regularity
Zoom (pedir link a Raimundo Briceño)
2020-06-01
16:30hrs.
Aníbal Velozo. Yale University
Suspension Flows over Countable Markov Shifts
Zoom (pedir link a Raimundo Briceño)
2020-05-11
16:30hrs.
Nishant Chandgotia. Hebrew University of Jerusalem
Predictive Sets
Zoom (pedir link a Raimundo Briceño)
2020-05-04
16:30hrs.
François Maucourant. Irmar, Université de Rennes 1
Dynamics of Unipotent Frame Flows on Hyperbolic Manifolds
Zoom (pedir link a Raimundo Briceño)
2019-11-25
14:30--15:30hrs.
Yixiao Qiao. Mean Dimension and The Embedding Problem
Mean dimension and the embedding problem
CMM (Beauchef 851, Torre Norte, 7mo piso, Sala de Seminarios John Von Neumann)
Abstract:
Mean dimension is a topological invariant other than topological entropy in the study of dynamical systems. It was introduced by Misha Gromov with a view towards geometric analysis around 1998, and was systematically developed by Elon Lindenstrauss and Benjy Weiss around 2000 with applications to topological dynamics. Meanwhile, mean dimension theory is very close to the embedding problem, i.e., embedding topological dynamical systems in Hilbert cubes. In this talk, I will present historical results and recent progress of the embedding problem as well as open problems in this direction.
2019-11-18
14:30hrs.
Jonathan Conejeros Lagos. Usach
Aplicaciones de la teoría de forzamiento para los homeomorfismos del anillo compacto
Beauchef 851, Torre Norte, 7mo piso, Sala de Seminarios John Von Neumann
Abstract:
En esta charla presentaremos una introducción a la teoría de forzamiento de trayectorias transversas para homeomorfismos de superficie. Usando esta teoría, estudiamos los conjuntos de rotación de los homeomorfismos del anillo compacto que son isotópicos a la identidad. Probamos que si un tal homeomorfismo preserva el área, entonces todo número en su conjunto de rotación es realizado por un conjunto compacto e invariante. Trabajo con Fábio Tal.      
2019-11-11
14:30hrs.
Rodolfo Gutiérrez . Uch
Lower bounds on the Hausdorff dimension of the Rauzy gasket
CMM (Beauchef 851, Torre Norte, 7mo piso, Sala de Seminarios John Von Neumann)
Abstract:
The Rauzy gasket is an important fractal object arising in several dynamical constructions, such as Novikov's problem and some renormalization schemes for certain families of interval exchange maps. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension D of the Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed the upper bound D 1.19. This is joint work with Carlos Matheus.
2019-10-14
16:50-17:50hrs.
Pablo Aguirre. Utfsm, Chile
Nonlinear dynamics of propagation and containment of dengue
Sala C506 (Construcción Civil 5to piso), Av. Vicuña Mackenna 4860, Macul, La Florida.
Abstract:
Arboviruses such as dengue, zyka and chikungunya are viruses transmitted to humans by mosquitoes. In particular, Aedes Aegypti mosquito is the responsible for dengue transmission. In the absence of medical treatments and vaccines, one of the control methods is to introduce Aedes Aegypti mosquitoes infected by the bacterium Wolbachia into a population of wild (uninfected) mosquitoes. The goal consists in achieving population replacement in finite time by driving the population of wild mosquitoes towards extinction while keeping Wolbachia-infected mosquitoes alive. This strategy has several advantages for control of dengue: Wolbachia decreases the virulence of the dengue infection and it reduces the lifespan of the mosquito. Moreover, mating of a female uninfected by Wolbachia and an infected male leads to sterile eggs. We consider a competition model between wild Aedes Aegypti female mosquitoes and those infected with the bacteria Wolbachia in the form of a system of nonlinear differential equations. Our goal is to examine the basin of attraction of a desired equilibrium state. For this purpose, we study how the stable manifold that forms the basin boundary of interest changes under parameter variation. To achieve this, we combine analytical tools from dynamical systems and geometric singular perturbation theory with numerical continuation methods. This allows us to present a strategy to get the desired population replacement with a minimum amount of released infected mosquitoes in a human, external intervention by choosing an appropriate combination of initial conditions and parameter values.
2019-10-14
14:30-15:30hrs.
Victor Nopal Coello. Cimat, México
Construction of Herman n-rings from Siegel disk on C_p
Sala C506 (Construcción Civil 5to piso), Av. Vicuña Mackenna 4860, Macul, La Florida.
Abstract:
Let $R$ be a rational map of degree $d\geq 2$ with coefficients in the non-Archimedean field $C_p$, with $p$ a prime number. Assume that the Fatou set $F_R$ associated to $R$ contains an m-cycle of Siegel disk, say $D_1, D_2, ..., D_m$. In this talk I will explain how to build a racional map $Q$ of degree $d+1$ with coefficients on $C_p$ and such that $F_Q$ contains an $m$-cycle of Herman $n$-ring coming from the Siegel disks of $F_R$
2019-10-14
15:45-16:45hrs.
Van Tu Le. Imt, Francia
Fixed points of post-critically algebraic endomorphisms
Sala C506 (Construcción Civil 5to piso), Av. Vicuña Mackenna 4860, Macul, La Florida.
Abstract:
A holomorphic endomorphism of $\mathbb{CP}^n$ is post-critically algebraic if its critical hypersurfaces are periodic or preperiodic. This notion generalizes the notion of post-critically finite rational maps in dimension one. We will study the eigenvalues of the differential of such a map at its fixed points. When $n=1$, a well-known fact is that the eigenvalue at a fixed point is either superattracting or repelling. We prove that when $n=2$ the eigenvalues are still either superattracting or repelling. This is an improvement of a result by Mattias Jonsson. When $n \geq 2$ and the fixed point is outside the post-critical set, we prove that the eigenvalues are repelling. This result improves one which was already obtained by Fornaess and Sibony under a hyperbolicity assumption on the complement of the post-critical set.
 
2019-10-07
15:30hrs.
Italo Cipriano. PUC
Construction of a noninvertible minimal map
Sala 1, PUC, Facultad de Matemáticas
Abstract:
In 1979 Susan Mary Rees (coauthor of prof Jan) wrote a construction of a noninvertible minimal map, answering a question by Furstenberg. One year earlier, she had finished her PhD thesis under the supervision of prof Bill Parry. The construction of Rees consists of a very clever ''surjery'' of a minimal homeomorphism of the 2-torus. Her paper is very hard to read and many steps were left to the reader. Surprisingly, the first reference to her work appeared only in 2001, since then it has been cited regularly. In this talk, I will speak about the main steps of the original construction by Rees, using as reference the paper of Kolyada, Snoha and Trofimchuk in 2001, where all the details of the proof were filled and the original construction was finally completed.