Thursday, May 14, 2020

Open sets of partially hyperbolic systems having a unique SRB measure

Davi Obata
(Université Cergy-Pontoise)

Abstract: For a dynamical system, a physical measure is an ergodic invariant measure that captures the asymptotic statistical behavior of the orbits of a set with positive Lebesgue measure. A natural question in the theory is to know when such measures exist. It is expected that a \"typical\" system with enough hyperbolicity (such as partial hyperbolicity) should have such measures. A special type of physical measure is the so-called hyperbolic SRB (Sinai-Ruelle-Bowen) measure. Since the 70`s the study of SRB measures is a very active topic of research. In this talk, we will see some new examples of open sets of partially hyperbolic systems with two dimensional center having a unique SRB measure. One of the key feature for these examples is a rigidity result for a special type of measure (the so-called u-Gibbs measure) which allow us to conclude the existence of the SRB measures.

Thursday, May 14, 2020
Time: 14h00
Room: TBA