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Article Dans Une Revue Communications in Mathematical Physics Année : 2006

Limit theorems in the stadium billiard

Résumé

We prove that the Birkhoff sums for "almost every" relevant observable in the stadium billiard obey a non-standard limit law. More precisely, the usual central limit theorem holds for an observable if and only if its integral along a one-codimensional invariant set vanishes, otherwise a root n log n normalization is needed. As one of the two key steps in the argument, we obtain a limit theorem that holds in Young towers with exponential return time statistics in general, an abstract result that seems to be applicable to many other situations.

Dates et versions

hal-00447501 , version 1 (15-01-2010)

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Citer

Peter Balint, Sébastien Gouëzel. Limit theorems in the stadium billiard. Communications in Mathematical Physics, 2006, 263 (2), pp.461-512. ⟨10.1007/s00220-005-1511-6⟩. ⟨hal-00447501⟩
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