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Measure of maximal entropy for finite horizon Sinai billiard flows

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Authors : Baladi, Viviane (Author of the conference)
CIRM (Publisher )

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Abstract : 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).

Keywords : billiard flows; measure of maximal entropy; transfer operators

MSC Codes :

    Information on the Video

    Film maker : Petit, Jean
    Language : English
    Available date : 02/11/2022
    Conference Date : 03/10/2022
    Subseries : Research talks
    arXiv category : Dynamical Systems ; Chaotic Dynamics
    Mathematical Area(s) : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:52:01
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-10-03_Baladi.mp4

Information on the Event

Event Title : Probabilistic techniques for random and time-varying dynamical systems / Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps
Event Organizers : Bahsoun, Wael ; Demers, Mark ; Nicol, Matthew ; Pène, Françoise ; Pollicott, Mark
Dates : 03/10/2022 - 07/10/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2601.html

Citation Data

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

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