Affiliation:
1. Department of Mathematics Fairfield University Fairfield Connecticut USA
2. Laboratoire de Probabilités Statistique et Modélisation (LPSM), Sorbonne Université, Université de Paris Paris France
Abstract
AbstractIn a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic properties for Hölder continuous observables, such as at least polynomial decay of correlations and the Central Limit Theorem. The results of Baladi and Demers are subject to a condition of sparse recurrence to singularities. We use a similar and slightly stronger condition, and it has a direct effect on our rate of decay of correlations. For billiard tables with bounded complexity (a property conjectured to be generic), we show that the sparse recurrence condition is always satisfied and the correlations decay at a super‐polynomial rate.
Funder
National Science Foundation
Horizon 2020
Engineering and Physical Sciences Research Council
Reference29 articles.
1. Positive Transfer Operators and Decay of Correlations
2. On the measure of maximal entropy for finite horizon Sinai Billiard maps
3. Thermodynamic formalism for dispersing billiards
4. P.BálintandI. P.Tóth An application of Young's tower method: exponential decay of correlations in multidimensional dispersing billiards Preprints of the Erwin Shrödinger International Institute for Mathematical Physics.https://www.esi.ac.at/preprints/esi2084.pdf 2008.
5. Chaotic scattering and diffusion in the Lorentz gas
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献