Volume 7 (2024)
Baladi, Viviane;  Carrand, Jérôme;  Demers, Mark F.
Measure of maximal entropy for finite horizon Sinai billiard flows
Annales Henri Lebesgue, Volume 7 (2024), pp. 727-747.

Metadata

DOI10.5802/ahl.209
Keywords Sinai billiard flow, finite horizon, measure of maximal entropy, equilibrium state

Abstract

Using recent work of Carrand on equilibrium states for the billiard map, and adapting techniques from Baladi and Demers, we construct the unique measure of maximal entropy (MME) for two-dimensional finite horizon Sinai (dispersive) billiard flows Φ 1 (and show it is Bernoulli), assuming the bound h top (Φ 1 )τ min >s 0 log2, where s 0 ∈(0,1) quantifies the recurrence to singularities. This bound holds in many examples (it is expected to hold generically).


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