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.

Description

Scholarly article / OA (arXiv PDF)

Keywords

Mathematics - Dynamical Systems

Citation

Bálint, P., Nándori, P., Szász, D., & Tóth, I. P. (2018). Equidistribution for standard pairs in planar dispersing billiard flows. Annales Henri Poincaré,19, pages 979–1042 (2018) https://doi-org.ezproxy.yu.edu/10.1007/s00023-018-0648-8