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Beyond Bowen specification property - lecture 1

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Authors : Climenhaga, Vaughn (Author of the conference)
CIRM (Publisher )

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Abstract : Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to specification" using a decomposition of the space of finite-length orbit segments, and then survey various applications, including factors of beta-shifts, derived-from-Anosov diffeomorphisms, and geodesic flows in non-positive curvature and beyond.

Keywords : measures of maximal entropy; expansivity; specification

MSC Codes :
37B10 - Symbolic dynamics
37B40 - Topological entropy
37D35 - Thermodynamic formalism, variational principles, equilibrium states

Additional resources :
https://www.cirm-math.fr/RepOrga/1947/Notes/Climenhaga-1-notes.pdf

    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 11/06/2019
    Conference Date : 14/05/2019
    Subseries : Research School
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:53:34
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-05-14_Climenhaga_Part1.mp4

Information on the Event

Event Title : Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity
Event Organizers : Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José
Dates : 13/05/2019 - 24/05/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/1947.html

Citation Data

DOI : 10.24350/CIRM.V.19525103
Cite this video as: Climenhaga, Vaughn (2019). Beyond Bowen specification property - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19525103
URI : http://dx.doi.org/10.24350/CIRM.V.19525103

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