 0577 P ter B lint and S bastien Gou zel
 Limit theorems in the stadium billiard
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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 nonstandard limit law.
More precisely, the usual central limit theorem holds for an
observable if and only if its integral along a onecodimensional
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.
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