Limit theorems in the stadium billiard

  • Bálint P
  • Gouëzel S
  • 8

    Readers

    Mendeley users who have this article in their library.
  • 34

    Citations

    Citations of this article.

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.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Péter Bálint

  • Sébastien Gouëzel

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free