- 06-104 N. Chernov and R. Markarian
- Dispersing billiards with cusps: slow decay of correlations
Apr 3, 06
(auto. generated ps),
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Abstract. Dispersing billiards introduced by Sinai are uniformly hyperbolic
and have strong statistical properties (exponential decay of
correlations and various limit theorems). However, if the billiard
table has cusps (corner points with zero interior angles), then its
hyperbolicity is nonuniform and statistical properties deteriorate.
Until now only heuristic and experiments results existed predicting
the decay of correlations as $\cO(1/n)$. We present a first rigorous
analysis of correlations for dispersing billiards with cusps.