Equidistribution for standard pairs in planar dispersing billiard flows
Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
YU Faculty Profile
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