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Rates of mixing for the measure of maximal entropy of dispersing billiard maps

Authors :
Demers, Mark F.
Korepanov, Alexey
Publication Year :
2022

Abstract

In 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 H\"older 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 super-polynomially.

Subjects

Subjects :
Mathematics - Dynamical Systems

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2204.04684
Document Type :
Working Paper