Noticias en español
Kieffer-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...
Read MoreOn the relation between topological entropy and asymptotic pairs.
ABSTRACT: I will present some results that state that under certain topological conditions, any action of a countable amenable group with positive topological entropy admits off-diagonal asymptotic pairs. I shall explain the latest results on this topic and present a new approach, inspired from thermodynamical formalism and developed in collaboration with Felipe García-Ramos and Hanfeng Li, which unifies all previous results and yields new classes of algebraic actions for which positive entropy yields non-triviality of their associated homoclinic group.
Read MoreDistorted diffeomorphisms and regularity.
ABSTRACT: The goal is to deal with the following question: for a compact manifold M, does there exist a diffeomorphism that is distorted in the group of C^r diffeomorphisms yet undistorted in the group of C^s diffeomorphism, where 1 \leq r < s ? Although the answer seems to be positive, it seems hard to build explicit examples (these diffeomorphisms necessarily have zero entropy). We will provide such examples for the closed unit interval for r = 1 and s = 2. The distortion part of the proof uses standard techniques on centralizers; the C^2 part uses recent work with Hélène Eynard on the...
Read MoreSuspension flows over countable Markov shifts.
ABSTRACT: Markov shifts have been systematically used to model discrete time dynamical systems with certain hyperbolicity. In the same spirit suspension flows over Markov shifts model some continuous time systems (e.g. uniformly hyperbolic flows on compact manifolds), where the flow has a transverse section with specified return time. In this talk I will discuss the entropy theory of the suspension flow over a countable Markov shift (a Markov shift with countable alphabet). I will focus on the entropy at infinity of the flow (a natural quantity in the non-compact case) and compactness of the...
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