Back to balls in billiards

Françoise Pene (1) , Benoit Saussol (1)

1 LM - Laboratoire de mathématiques de Brest

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.

Mots clés: billiard; Lorentz process; return time; hyperbolic with singularities; Young tower; local limit theorem.; local limit theorem

Domaines: Systèmes dynamiques [math.DS]

Françoise Pene, Benoit Saussol. Back to balls in billiards. 2009. ⟨hal-00349850⟩