Dynamical Day
3th June 2019

Facultad de Matemáticas UC, Santiago

The aim of this meeting is to gather a group of mathematicians working on dynamical systems to discuss new developments in the area.

Jairo Bochi
Italo Cipriano
Godofredo Iommi
Jan Kiwi
Mario Ponce

14:30-15:30 Anibal Velozo
15:45-16:45 Salomon Rebollo
16:50-17:50 Carlos Vasquez


Speaker: Anibal Velozo
Title: Pressure at infinity and applications. 
Abstract: There are many important dynamical systems which can be coded, via Markov partitions, into a symbolic dynamical system. Whenever this is possible one gets a fairly good understanding of the ergodic theory of the initial system. In this talk I will motivate the study of (non-compact) symbolic dynamics and elaborate on recent works about its entropy theory. I will focus on semi-continuity properties of the entropy and pressure. Notions of entropy and pressure at infinity play an important role in these results and will be discussed. This talk is partially based on joint works with G. Iommi and M. Todd.

Speaker: Salomon Rebollo
Title: Polynomial perturbations of planar vector fields with curves of singularities
Abstract: We will consider polynomial perturbations of planar polynomial vector fields that have centers and curves of singularities. For the perturbed vector field we will study its limit cycles that bifurcate from the centers of the unperturbed vector field. The bifurcation phenomena of limit cycles is richer in perturbation of vector fields with curves of singularities than in perturbation of vector fields with only isolated singularities. For example, more limit cycles can bifurcate in the former case than in the latter one. We will give some results about the maximum number of this kind of limit cycles that the perturbed vector field can support.

Speaker: Carlos Vásquez
Title: Invariance of entropy for maps isotopic to Anosov
Abstract: We prove the topological  remains constant inside the class of partially hyperbolic diffeomorphisms of $mathbb{T}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with ´´controlled geometry ´´) and such that their linear part is hyperbolic.
In absence of the simplicity condition it is possible to  construct a robustly transitive counter-example, evidencing the necessity of our assumptions.
Work in progress joint to Pablo Carrasco (UFMG-Brazil),  Cristina Lizana (UFBA -Brazil) and  E. Pujals (CUNY, USA).

This events is supported by CONICYT through the proyecto Anillo ACT172001 «New trends in ergodic theory» and by the Facultad de Matemáticas, Pontificia Universidad Católica de Chile