Equidistribution for standard pairs in planar dispersing billiard flows

Abstract

We prove exponential correlation decay in dispersing billiard flows on the 2-torus assuming finite horizon and lack of corner points. With applications aimed at describing heat conduction, the highly singular initial measures are concentrated here on 1-dimensional submanifolds (given by standard pairs) and the observables are supposed to satisfy a generalized Hölder continuity property. The result is based on the exponential correlation decay bound of Baladi et al. (Invent Math, 211:39–117, 2018. https://doi.org/10.1007/s00222-017-0745-1) obtained for Hölder continuous observables in these billiards. The model dependence of the bounds is also discussed.