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Stable laws for chaotic billiards with cusps at flat points
classification
math-ph
math.DSmath.MPmath.PR
keywords
billiardscuspflatstablevertexalphabilliardbirkoff
read the original abstract
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 H\"older continuous observables, we show that properly normalized Birkoff sums, with respect to the billiard map, converge in law to a totally skewed $\alpha$-stable law.
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