Dynamical Systems

Elementos de distorsión en el grupo de difeomorfismos de la esfera.

Event Date: Sep 16, 2020 in Dynamical Systems, Seminars

ABSTRACT: En esta charla estudiaremos algunas propiedades dinámicas, fuera del mundo de la medida, de los elementos de distorsión en el grupo de difeomorfismos de la esfera.

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Modelos topológicos de sistemas loosely Bernoulli con entropía cero.

Event Date: Sep 09, 2020 in Dynamical Systems, Seminars

ABSTRACT: Daremos una caracterización puramente topológica de sistemas dinámicos únicamente ergódicos cuya medida tiene entropía cero y es loosely Bernoulli. Para esto usaremos la pseudo métrica de Feldman-Katok. Algunos ejemplos que caen en esta categoría son horociclos, sistemas de rango finito y distales. Trabajo en conjunto con Dominik Kwietniak.

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Dimension theory for continued fractions.

Event Date: Sep 02, 2020 in Dynamical Systems, Seminars

ABSTRACT: Every real number can be written as a continued fraction. There exists a dynamical system, the Gauss map, that acts as the shift in the expansion. In this talk, I will comment on the Hausdorff dimension of two types of sets: one of them defined in terms of arithmetic averages of the digits in the expansion and the other related to (continued fraction) normal numbers. In both cases, the non compactness that steams from the fact that we use countable many partial quotients in the continued fraction plays a fundamental role. Some of the results are joint work with Thomas Jordan and...

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Derivadas de valores propios y exponentes de Lyapunov.

Event Date: Aug 26, 2020 in Dynamical Systems, Seminars

ABSTRACT: Voy a presentar un ejemplo simple, como calcular derivadas de la aplicación que asocia a una matriz en GL(n,R) un valor propio simple. Partiendo del ejemplo voy a hablar sobre las derivadas de exponentes de Lyapunov para difeomorfismos con descomposición dominada, y una aplicación para la entropía métrica.

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Intermediate entropy property: old and new.

Event Date: Aug 19, 2020 in Dynamical Systems, Seminars

  ABSTRACT:  A dynamical system verifying the intermediate entropy property is one such that any value between 0 and the topological entropy is realized as the measure-theoretical entropy of some ergodic measure. In this talk I will present an overview of the main results involving this property, taking as a starting point a conjecture of Katok and ending by a potpourri of recent results.  

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Kieffer-Pinsker type formulas for Gibbs measures.

Event Date: Jul 13, 2020 in Dynamical Systems, Seminars

ABSTRACT:  In this talk I will present ongoing work regarding new expressions for entropy and pressure in the context of Gibbs measures defined over countable groups. Our starting point will be the Pinsker formula for the Kolmogorov-Sinai entropy of measure preserving actions of orderable amenable groups. Then, we will consider a formula for pressure that was developed by Marcus-Pavlov (2015) and B. (2018). Next, we will review some techniques based on random orderings, mixing properties of Markov random fields, and percolation theory in order to generalize previous work by introducing what...

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