Back to balls in billiards
Dynamical Systems
2015-05-13 v1
Abstract
We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed to get back in an r-ball about the initial point, in the phase space and also for the position, in the limit when r->0. We establish the existence of an almost sure convergence rate, and prove a convergence in distribution for the rescaled return times.
Keywords
Cite
@article{arxiv.0901.0441,
title = {Back to balls in billiards},
author = {Françoise Pène and Benoit Saussol},
journal= {arXiv preprint arXiv:0901.0441},
year = {2015}
}