05-77 P ter B lint and S bastien Gou zel

Limit theorems in the stadium billiard (658K, pdf) Feb 23, 05

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Abstract. 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 $\sqrt{n\log n}$ 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.

Files: 05-77.src( 05-77.keywords , stadium9.pdf.mm )