Measure of maximal entropy for finite horizon Sinai billiard flows

Viviane Baladi, Jérôme Carrand, Mark Demers

Published 2022-09-02Version 1

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).