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 [InlineMediaObject not available: see fulltext.] 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Bálint, P., & Gouëzel, S. (2006). Limit theorems in the stadium billiard. Communications in Mathematical Physics, 263(2), 461–512. https://doi.org/10.1007/s00220-005-1511-6
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