Communications in Mathematical Physics

, Volume 263, Issue 2, pp 461–512

Limit Theorems in the Stadium Billiard

Article

DOI: 10.1007/s00220-005-1511-6

Cite this article as:
Bálint, P. & Gouëzel, S. Commun. Math. Phys. (2006) 263: 461. doi:10.1007/s00220-005-1511-6

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 https://static-content.springer.com/image/art%3A10.1007%2Fs00220-005-1511-6/MediaObjects/s00220-005-1511-6flb1.gif 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.IRMARUniversité de Rennes 1Rennes CedexFrance