Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows

Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-018-0648-8
Publisher site
See Article on Publisher Site

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.

Journal

Annales Henri PoincaréSpringer Journals

Published: Feb 17, 2018

References

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