EVENT DETAILS AND ABSTRACT

Title: Decay of correlations for nonuniformly hyperbolic billiards
Speaker: Hongkun Zhang
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

Billiards are dynamical systems originating the study of Boltzmann's Ergodic Hypothesis in statistical mechanics. For nonuniformly hyperbolic billiards, it is very important to determine the rate of convergence of sequence of distributions to equilibrium state. We introduce a new one-step expansion condition, and show the reduced map of billiard map on a uniformly hyperbolic set enjoys exponential decay of correlations. The main method we use is to couple distributions supported on two families of unstable curves, and show the couple rate is exponentially fast.