Stable laws for chaotic billiards with cusps at flat points
Mathematical Physics
2018-09-20 v3 Dynamical Systems
math.MP
Probability
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 -stable law.
Cite
@article{arxiv.1611.00879,
title = {Stable laws for chaotic billiards with cusps at flat points},
author = {Paul Jung and Hongkun Zhang},
journal= {arXiv preprint arXiv:1611.00879},
year = {2018}
}
Comments
42 pages. The paper has been revised to improve presentation, correct typos, and fix an error in what is now Proposition 4.2. To appear in Annales Henri Poincar\'e