Collection Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity

Organizer(s) Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José

Date(s) 13/05/2019 - 24/05/2019

linked URL https://conferences.cirm-math.fr/1947.html

3 9

Beyond Bowen specification property - lecture 1

By Vaughn Climenhaga

Also appears in collection : Dynamique au-delà de l’hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity

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.

Information about the video

Date of recording 14/05/2019
Date of publication 11/06/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19525103
Cite this video Climenhaga, Vaughn (14/05/2019). Beyond Bowen specification property - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19525103
URL https://dx.doi.org/10.24350/CIRM.V.19525103

Domain(s)

Dynamical Systems

Bibliography

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