## Assouad dimension of planar self-affine sets

ABSTRACT: We consider planar self-affine sets X satisfying the strong separation condition and the projection condition. We show that any two points of X, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets. We also calculate the Assouad dimension of X. Finally, we prove that if X is dominated, then it is minimal for the conformal Assouad dimension. The talk is based on joint work with Balázs Bárány and Eino Rossi.

Read More## Algebraic invariant of minimal group actions on the Cantor set: topological full group and group of automorphism

Read More## SEMINAR DYNAMICAL SYSTEMS THE SANTIAGO & SEMINAR KAWIN

Seminario Kawin TIME (Mon 22th Apr) 3:30 pm – 4:20 pm LOCATION USACH, Sala de seminarios del 4to piso del Departamento de Matemáticas y Ciencia de la computación ( Las Sophoras nº 173, Santiago, Estación Central). SPEAKER Cristobal Rivas (USACH) TITLE Sobre el grupo de Higman ABSTRACT Les contaré sobre el grupo de Higman. Porqué no tiene cocientes finitos y porqué no admite representaciones lineales. Si aún hay tiempo, diré algunas palabras sobre sus representaciones en grupos de difeomorfismos y homeomorfismos. Seminario Sistemas Dinámicos de Santiago. TIME ...

Read More## Counting problem on infinite periodic billiards and translation surfaces

ABSTRACT The Gauss circle problem consists in counting the number of integer points of bounded length in the plane. This problem is equivalent to counting the number of closed geodesics of bounded length on a flat two dimensional torus or, periodic trajectories, in a square billiard table. Many counting problems in dynamical systems have been inspired by this problem. For 30 years, the experts try to understand the asymptotic behavior of closed geodesics in translation surfaces and periodic trajectories on rational billiards. (Polygonal billiards yield translation surfaces naturally through...

Read More## On subsets with no arithmetic progressions

ABSTRACT For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a subset of \{1,\ldots,N\} that contains no arithmetic progression of length 3. Finding upper and lower bounds for $\nu(N)$ has been a challenging problem for decades. In this talk I will survey this problem and present a proof of a theorem by Behrend in the 40’s, that gave a surprising lower bound to $\nu(N)$.

Read More## Understanding physical mixing processes via transfer operator approach

ABSTRACT: Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications.In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint. In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introductionon the relationships between the spectral properties of the associated transfer operator and the estimations of the optimal mixing rate of the mixing process. Moreover,...

Read More