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Annales Henri Poincaré

, Volume 9, Issue 1, pp 91–107 | Cite as

Sinai Billiards under Small External Forces II

  • Nikolai ChernovEmail author
Article

Abstract.

We study perturbations of Sinai billiards, where a small stationary force acts on the moving particle between its collisions with scatterers. In the previous work [7] we proved that the collision map preserved a unique Sinai–Ruelle–Bowen (SRB) measure that was Bernoulli and had exponential decay of correlations. Here we add several other statistical properties, including bounds on multiple correlations, the almost sure invariance principle (ASIP), the law of iterated logarithms, and a Kawasaki-type formula. We also show that the corresponding flow is Bernoulli and satisfies a central limit theorem.

Keywords

Central Limit Theorem Open Loop Unstable Manifold Iterate Logarithm Stable Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

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