Dispersing billiards with cusps: slow decay of correlations
نویسندگان
چکیده
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 O(1/n). We present a first rigorous analysis of correlations for dispersing billiards with cusps.
منابع مشابه
Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows
Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick succession, it is reasonable to expect a much faster decay rate in continuous time. In this paper we prove that the flow is rapid mixing: correlations decay faster ...
متن کامل0 M ay 2 00 8 Decay of correlations and invariance principles for dispersing billiards with cusps , and related planar billiard flows
Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick succession, it is reasonable to expect a much faster decay rate in continuous time. In this paper we prove that the flow is rapid mixing: correlations decay faster ...
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