Back to balls in billiards

Details Back to balls in billiards Back to balls in billiards

2009-01-05

arxiv.org/abs/0901.0441v1

Mathematics

Dynamical Systems

Scientific paper

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.

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