Noticias en español
Dimension theory for continued fractions.
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...
Read MoreDerivadas de valores propios y exponentes de Lyapunov.
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.
Read MoreIntermediate entropy property: old and new.
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.
Read MoreKieffer-Pinsker type formulas for Gibbs measures.
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...
Read MoreAcciones de grupos localmente desplazantes.
Resumen: Rubin introdujo la noción de grupo localmente desplazante (locally moving) y encontró muchos teoremas de “reconstruccion” del espacio a partir de la acción del grupo. En particular, un grupo admite una unica accion localmente desplazante salvo conjugación. La clase de grupos localmente desplazantes contiene desde grupos muy grandes como Difeos(R) a grupos pequeños, incluso finitamente presentados, como el grupo de Thompson F. Tienen en común, que todos admiten una acción dinámicamente rica. En un trabajo en conjunto con Brum, Matte-Bon y Triestino, nos interesamos en...
Read MoreStabilizers in group Cantor actions and measures.
ABSTRACT: Given a countable group G acting on a Cantor set X by transformations preserving a probability measure, the action is essentially free if the set of points with trivial stabilizers has full measure. On the other hand, there are many examples of group actions, where every point has a non-trivial stabilizer. In this talk, we generalize the notion of an essentially free action to such actions, using the notion of holonomy. For equicontinuous actions of countable groups on Cantor sets, we answer the following question: under what conditions there exists a subgroup H of G, such that...
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