Recent Progress in the Application of Transfer Operators to Dispersing Billiards

Abstract

This is a review paper about the use of transfer operators to study the statistical properties of hyperbolic billiards. The main focus is on equilibrium states, sequential billiards, and decay of correlation for billiard flows. In addition to reviewing the literature, we try to flesh out the main ideas, highlight the relations between them, and provide the larger context in which the problems discussed here are situated.