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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 pha...

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Bibliographic Details
Published in:Communications in mathematical physics 2010-02, Vol.293 (3), p.837-866
Main Authors: Pène, Françoise, Saussol, Benoît
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-009-0911-4