EVENT DETAILS AND ABSTRACT

Title: SRB measures and Young towers for surface diffeomorphisms
Speaker: Vaughn Climenhaga
Speaker Info: University of Houston
Brief Description:
Special Note:
Abstract:

Existence and statistical properties of Sinai-Ruelle-Bowen measures is a central problem in non-uniform hyperbolicity. Lai-Sang Young showed that existence of a certain "tower" is a sufficient condition for existence of an SRB measure, and that statistical properties of the measure can be deduced from examining the "tail" of the tower. I will discuss joint work with Ya. Pesin and S. Luzzatto, in which we consider the two-dimensional case and show that Young's condition is not only sufficient but is also necessary; that is, every SRB measure lifts to a first return Young tower with integrable tails. This gives a symbolic representation of the dynamics in terms of a countable alphabet. Our construction works not just for SRB measures but also for every hyperbolic ergodic measure; I will also describe expected applications to statistical properties of geodesic flow over surfaces of nonpositive curvature.