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Authors: | Fran?oise Pène Beno?t Saussol |
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Institution: | 1. Université Européenne de Bretagne, Brest, France 2. Université de Brest, Laboratoire de Mathématiques, CNRS UMR 6205, 6 avenue Victor Le Gorgeu, F-29238, Brest, France
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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 ε-ball about the initial point, in the phase space and also for the position, in the limit when ε → 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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