Measure of maximal entropy for finite horizon Sinai billiard flows
Dynamical Systems
2024-09-26 v2 Chaotic Dynamics
Abstract
Using recent work of Carrand on equilibrium states for the billiard map, and bootstrapping via a "leapfrogging" method from a previous article of Baladi and Demers, we construct the unique measure of maximal entropy for two-dimensional finite horizon Sinai (dispersive) billiard flows (and show it is Bernoulli), assuming that the topological entropy of the flow is strictly larger than s_0 log 2 where 0<s_0<1 quantifies the recurrence to singularities. This bound holds in many examples (it is expected to hold generically).
Keywords
Cite
@article{arxiv.2209.00982,
title = {Measure of maximal entropy for finite horizon Sinai billiard flows},
author = {Viviane Baladi and Jérôme Carrand and Mark Demers},
journal= {arXiv preprint arXiv:2209.00982},
year = {2024}
}
Comments
Version v2 is the electronic copy of the version to appear in Ann. H. Lebesgue