Measure of maximal entropy for finite horizon Sinai billiard flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909324475891712 |
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| author | Baladi, Viviane Carrand, Jérôme Demers, Mark |
| author_facet | Baladi, Viviane Carrand, Jérôme Demers, Mark |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00982 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Measure of maximal entropy for finite horizon Sinai billiard flows Baladi, Viviane Carrand, Jérôme Demers, Mark Dynamical Systems Chaotic Dynamics Subjects: 37C83 (Primary) 37D35, 37C30, 37D40, 37B40 (Secondary) 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). |
| title | Measure of maximal entropy for finite horizon Sinai billiard flows |
| topic | Dynamical Systems Chaotic Dynamics Subjects: 37C83 (Primary) 37D35, 37C30, 37D40, 37B40 (Secondary) |
| url | https://arxiv.org/abs/2209.00982 |