Dynamical Resistance Day

Margulis measures on foliations and measures of maximal entropy
25 de Setembro | 11h00min | Ali Tahzibi (ICMC USP São Carlos, Brazil)

Title: Margulis measures on foliations and measures of maximal entropy (video)

Bowen-Margulis measure for uniformly hyperbolic dynamics stands for measure of maximal entropy. The approach by Bowen was using periodic measures and Margulis in his thesis constructed maximal entropy measures for Anosov flows using a geometric construction.

In the context of partially hyperbolic dynamics, there are few results on the uniqueness (finiteness) of measures of maximal entropy, when they exist. In this talk, we recall some progress in partially hyperbolic setting and focus mainly on the following:

We explored the Margulis approach to the context of flow type partially hyperbolic dynamics, in particular diffeomorphisms close to time-one map of Anosov flows. We obtained a dichotomy, proving either just non-hyperbolic or exactly two hyperbolic ergodic measures of maximal entropy for such diffeomorphisms. These works are in collaboration with J. Buzzi and T. Fisher and J.Buzzi, Crovisier and Poletti.