Edson Vargas

• Abstract

  Wandering domains construction by explosion of orbits in hyperbolic homoclinic classes for diffeomorphisms on compact surfaces. (AU)

  Wandering domains for bidimensional dynamics, AV.EXT

• Abstract

  The main goal of this project is to prove that invariant measures for weakly hyperbolic diffeomorphisms and flows with singularities can be approximated on the weak topology by periodic measures supported on hyperbolic periodic orbits. This result extends results we proved before and have applications in the context of dispersing billiards. This project is a continuation of some recent pu…

  Invariant measures in weakly hyperbolic dynamics, AV.EXT

• Abstract

  This project has two parts: 1. The study of the continuity of the topological entropy and of the metric entropy for partially hyperbolic systems with low dimensional center and the regularity of Lyapunov exponents associated to invariant bundles. 2. Classification of partially hyperbolic systems with one-dimensional center and eventual density of periodic orbits in the nonwandering set. (…

  Continuity of entropy and classification of partially hyperbolic systems with one-dimensional central bundle, AV.EXT

(Only some records are available in English at this moment)

• Abstract

  The aim of this research is to consider the existence of wandering intervals for the class ofcircle homeomorphisms with critical points withmixed criticality. By this we mean that thecriticality as we approach the critical pointfrom above is not equal to the criticality as weapproach from below. Such maps occur naturally inthe study of flows on surfaces with saddle connections.Once the to…

  Dynamics with critical points of mixed criticality, BP.PD

• Abstract

  For critical covering maps of the circle we shall describe the set of accumulation points of the sequence of Birkhoff averages of the Lebesgue measure. The maps for which the above sequence has just one accumulation point, called physical measure, will be of special interest.

  Physical measures for critical covering maps of the circle, BP.DR

• Abstract

  We are interested on generic properties of certain low dimensional dynamical systems. For example, the relation between parcial and nonuniform hyperbolicity for diffeomorphisms on a generic set and the homology of invariant foliations for parcially hyperbolic diffeomorphisms are questions we plan to attack.

  Generic properties of diffeomorphisms in low dimensions, BP.PD

(Only some records are available in English at this moment)

• Abstract

  We are going to work on three types of dynamical systems which have been a fruitful subject of our recent research. The first is about physical measures, irregular set and wandering domains for diffeomorphisms dynamics. The second is about full families of multimodal rational maps on the circle. The third is about the renormalization operator in the context of Feidenbaun-Coullet-Tresser …

  Three dynamics, three questions, BE.PQ