Stable laws for chaotic billiards with cusps at flat points. (English) Zbl 1407.37058
Summary: We consider billiards with a single cusp where the walls meeting at the vertex of the cusp have zero one-sided curvature, thus forming a flat point at the vertex. For Hölder continuous observables, we show that properly normalized Birkhoff sums, with respect to the billiard map, converge in law to a totally skewed \({\alpha}\)-stable law.
MSC:
| 37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
| 60F05 | Central limit and other weak theorems |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
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