Measure of maximal entropy for finite horizon Sinai billiard flows | Vidéo | Carmin.tv

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Measure of maximal entropy for finite horizon Sinai billiard flows

By Viviane Baladi

Appears in collection : Probabilistic techniques for random and time-varying dynamical systems / Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps

The SRB measure of Sinai billiard maps and flows has been studied for decades, but other equilibrium states have been investigated only recently. Assuming finite horizon, the measure of maximal entropy (MME) of the (discontinuous) map has been constructed and shown to be unique and Bernoulli (joint work with Demers, 2020), under a mild condition (believed to be generic) on the topological entropy. Demers and Korepanov have recently shown that this MME mixes at least polynomially (for H¨older observables). In spite of the continuity of the billiard flow, the mere existence of the MME for the flow has been a challenging problem. I will explain how we obtain existence, uniqueness and Bernoullicity of the MME of the Sinai billiard flow, assuming finite horizon and a mild condition (also believed to be generic), by bootstrapping on very recent work of J´erˆome Carrand about a family of equilibrium states for the billiard map. We use transfer operators acting on anisotropic Banach spaces. (Joint work with J´erˆome Carrand and Mark Demers).

Information about the video

Date of recording 03/10/2022
Date of publication 02/11/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.19964503
Cite this video Baladi, Viviane (03/10/2022). Measure of maximal entropy for finite horizon Sinai billiard flows. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19964503
URL https://dx.doi.org/10.24350/CIRM.V.19964503

Domain(s)

Bibliography

BALADI, Viviane, CARRAND, Jérôme, et DEMERS, Mark. Measure of maximal entropy for finite horizon Sinai billiard flows. arXiv preprint arXiv:2209.00982, 2022. - https://doi.org/10.48550/arXiv.2209.00982

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