Seminario de Sistemas Dinámicos

2011-03-07

Jairo Bochi. Puc-Rio de Janeiro
Uniform Hyperbolicity and Gap Opening
CENI-USACH (sala por confirmar
Abstract:
The study of products of random matrices naturally leads to the concept of a linear cocycle over a dynamical system endowed with an invariant probability measure. The asymptotic growth of these matrix products is described in terms of Lyapunov exponents by Oseledets theorem.

The simplest interesting case is given by matrices in SL(2,R). In that case, the cocycle is called uniformly hyperbolic if the matrix products grow uniformly exponentially with length. This is equivalent to the existence of uniformly expanding and contracting subbundles a la Smale.

In this talk I will consider SL(2,R)-cocycles over strictly ergodic dynamics (that is, uniquely ergodic dynamics with an invariant measure of full support).

I will explain when such a cocycle can be C^0-approximated by a uniformly hyperbolic

2011-01-10

Yves de Cornulier. Université Paris Sud, Orsay
Contaje de Clases de Conjugacion en Grupos Lineales
Sala 2 (víctor Ochsenius) - Facultad de Matemáticas - PUC

2011-01-03

Weixiao Shen. National University of Singapur
On stochastic stability of non-uniformly expanding interval maps
Sala 2 (Víctor Ochsenius) Fac. de Matemáticas PUC 16:230 hrs.
Abstract:
We shall discuss stochastic stability with respect to additive nosie for regular intervals that satisfies a summability condition. This is based on a careful analysis on the derivative growth along pesudo-orbits which has potential applications to other problems related to perturbation of non-uniformly expanding interval maps.

2010-12-10

Yann Bugeaud. Université de Strasbourg
On the decimal expansion of algebraic numbers
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas PUC - 16:30 hrs.
Abstract:
Classical ways to represent a real number are by its continued fraction
expansion or by its expansion in some integer base. It is commonly
expected that algebraic irrational numbers behave, in many respects, like almost all numbers. For instance, their decimal expansion should contain every finite block of digits from ${0, ldots , 9}$. We are very far away from establishing such a strong assertion. However, there has been some recent progress, that will be surveyed in the lecture.

2010-11-23

Raphael Krikorian. École Polytechnique, France
Lyapunov exponents of quasi-periodic cocycles non-homotopic to the identity: regularity and rigidity
Sala de Reuniones, Decanato Facultad de Ciencia, USACH
Abstract:
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2010-11-22

Alexis Ballier. Cmm-Universidad de Chile
Computing (or not) quasi-periodicity of tilings
Sala de Seminarios 7mo piso, CMM-U. de Chile - 17:00
Abstract:
We know that, in any dimension, any subshift contains a configuration that is uniformly recurrent (or quasi-periodic): a configuration for which any pattern that appears must appear in every sufficiently large part of the configuration. One can then define the recurrence function q of an uniformly recurrent configuration as a function from N into itself such that q(n) is the smallest integer in which any pattern of size q(n) contains every pattern of size n.

This function is a way to measure the regularity of an uniformly recurrent configuration and, to some extent, of a subshift since it must contain at least one such configuration. Since even subshifts of finite type (SFTs) hold many uncomputable properties, one can expect this function to inherit some of these

2010-11-15

Samuel Senti. Ufrj Brasil
Lifting measures to inducing schemes
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Inducing schemes are used in dynamical systems in order to find a symbolic coding of a subset of the phase space. The induced map - defined on each element of the inducing scheme as an iterate of the original map on - is conjugated to the full symbolic shift on a countable alphabet. Although certain ergodic properties of the full shift carry over to original map, there is no one to one correspondence between invariant probabilities of the shift and those of the original map. The liftability problem consists in studying which measures have shift invariant counterparts. We study the problem for piecewise continuous maps of compact metric spaces. Time permitting we will present some ideas towards dealing with the higher dimensional cases

2010-11-08

Karl-Olof Lindahl. Linnaeus University, Sweden
The Siegel Center Problem in Ultrametric Dynamics
Sala 2 (Víctor Ochsenius), Facultad de Matemáticas PUC - 16.30 hrs.
Abstract:
We consider the `Siegel center problem´ (i.e. local linearization of power series about indifferent fixed points) for ultrametric fields. It is known since a paper of Herman and Yoccoz in 1981 that Siegel´s linearization theorem for the complex field case is true also for ultrametric fields. They also showed that there exist examples in fields of prime characteristics where the Siegel, nor the weaker Brjuno condition is satisfied, imposing a problem of small divisors. However, until recently, it was still an open question whether these small divisors yield divergence of the corresponding conjugacy or not. In fact, it has been shown that the same multiplier may yield divergence of the conjugacy for some analytic functions and convergence for others. In other words,

2010-10-28

Katrin Gelfert. Universidade Federal de Rio de Janeiro
Thermodynamics for geodesic flows
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas - 16.30 hrs
Abstract:
Abstract: I will talk about some properties of geodesic flows of a compact surface in the case that the flow is non-uniformly hyperbolic.

2010-10-25

Juan Rivera Letelier. Pontificia Universidad Católica de Chile
Potenciales Estocásticos de Aplicaciones del Intervalo
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.

2010-09-13

Irene Inoquio. Universidad Católica del Norte, Antofagasta
Sobre el formalismo termodinámico de una aplicación racional
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas PUC - 16:30 hrs.
Abstract:
Resumen: Estudiamos el formalismo termodinámico de una aplicación racional $f$ actuando sobre la esfera de Riemann, de grado a lo menos 2. Dado un potencial Hölder continuo $varphi$ satisfaciendo la siguiente condición $sup varphi Para una función racional $f$ nosotros caracterizamos estos potenciales Hölder continuos de tal manera que esta propiedad es satisfecha para algún iterado de la función $f$.

2010-09-06

José Alves. Universidade de Porto, Portugal
de Las Tasas de Mezcla a los Tiempos de Recurrencia
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas UC - 16:30 Hrs.

2010-08-16

Ayse Sahin Berksoy. Depaul University, Chicago.
Directional entropy, rank one Z^d actions and restricted orbit equivalence
Sala de Seminarios 7mo piso, CMM-UdeChile - 17:00 Hrs.
Abstract:
Resumen:
We study the dynamical properties of Z^d rank one actions as a function of the geometry of the shapes of the towers generating the action. The main results relate the geometry to the possible directional entropies of the action. In recent work we also showed a connection between directional entropy and the restricted orbit equivalence classification of group actions. The talk will describe these results and will present a historical overview of orbit equivalence theory. These results were obtained in joint work with E. Arthur Robinson, Jr.

2010-08-09

José Aliste. Cmm-Dim Udechile
Sobre la existencia de semiconjugaciones a translaciones minimales
Sala de seminarios 7mo piso, CMM UdeChile.- 17:00 Hrs.
Abstract:

Resumen: Estudiamos una clase de sistemas preservando una foliación por rectas y mostramos que uno de estos sistemas es semi conjugado a una translación minimal si y solo si se tiene una condición de acotamiento en el desplazamiento. La clase de sistemas estudiado incluye: productos torcidos sobre flujos quasiperiodicos o casi-periodicos, transformaciones en espacios de embaldosados aperiódicos, transformaciones de la recta con desplazamientos casi-periodicos.

Trabajo en conjunto con Tobias Jäger (TU Dresden

2010-07-26

Edgardo Ugalde. Instituto de Física -- Universidad Autónoma de San Luis Potosí
Convergencia al Estado Base en Sistemas Unidimensionales
Sala de seminarios, 7mo piso CMM. - 17:00 hrs.

2010-05-03

Mario Ponce. Pontificia Universidad Católica de Chile
Flores fibradas (o el estudio de curvas invariantes parabólicas
Sala 2 (Víctor Ochsenius)- Facultad de Matemáticas - UC
Abstract:
Resumen: Consieramos una dinámica holomorfa fibrada admitiendo una curva invariante parabólica. Mostramos que bajo ciertas condiciones, aparecen, como en el caso clásico, flores fibradas adosadas a la curva. Sin embargo, varios fenómenos interesantes pueden ocurrir y la determinación combinatoria de la flor es más rica y compleja que la teoría clásica de Leau y Fatou.

2010-04-19

Gabriela Fernández. Puc-Uai
Linearización Global Para Acciones de $(Mathbb{C})^*)^n$ Con Singularidades Dicríticas en Variedades de Stein.
Sala 2 (Víctor Ochsenius) - Fac. de Matemáticas PUC - 16:30 Hrs.

2010-04-12

Alejandro Kocsard. Uff Brasil
Ecuaciones cohomológicas para difeomorfismos cuasiconformes
Sala de Seminarios del 7mo piso, CMM-UdeChile
Abstract:
Resumen: Dado cualquier difeomorfismo del círculo, con número de rotación irracional, mostraremos que su medida de probabilidad invariante es la única distribución invariante. Como una consecuencia mostraremos que el espacio de los cobordes diferenciables reales del difeomorfismo es cerrado si y solamente si el número de rotación es Diofantino. Mostraremos algunos contraejemplos en dimensión 2 o mayor.

2010-04-05

Godofredo Iommi. Pontificia Universidad Católica de Chile
Analisis Multifractal de Promedios de Birkhoff
Sala 2 (Víctor Ochsenius) - 16:30 Hrs. Facultad de Matemáticas - UC

2010-03-29

Alvaro Coronel. Pontificia Universidad Católica de Chile
Soluciones Medibles y en L² de Algunas Ecuaciones Cohomológicas Sobre Sistemas Dinámicos Asociados a Conjuntos de Delone.
Sala 2 (Víctor Ochsenius) - 16:30 Hrs. Facultad de Matemáticas - UC