10/05: Davi Obata
Open sets of partially hyperbolic systems having a unique SRB measure
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 has been 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 centers having a unique SRB measure. One of the key features for these examples is a rigidity result for a special type of measure (the so-called u-Gibbs measure) which allows us to conclude the existence of the SRB measures.