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AUDIOVISUAL MATHEMATICS LIBRARY

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Beyond Bowen specification property - lecture 2

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Multi angle
Auteurs : Climenhaga, Vaughn (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : 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

Codes MSC :
37B10 - Symbolic dynamics
 37B40 - Topological entropy
 37D35 - Thermodynamic formalism, variational principles, equilibrium states
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/1947/Notes/Climenhaga-2-notes.pdf
    Informations sur la Vidéo

    Réalisateur : Recanzone, Luca
    Langue : Anglais
    Date de publication : 11/06/2019
    Date de captation : 15/05/2019
    Sous collection : Research School
    arXiv category : Dynamical Systems
    Domaine : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Durée : 00:52:26
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-05-15_Climenhaga_Part2.mp4
Informations sur la Rencontre

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

Données de citation

DOI : 10.24350/CIRM.V.19525203
Citer cette vidéo: Climenhaga, Vaughn (2019). Beyond Bowen specification property - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19525203
URI : http://dx.doi.org/10.24350/CIRM.V.19525203

Voir aussi

Bibliographie

  • Jérôme Buzzi, Todd Fisher. Entropic stability beyond partial hyperbolicity. Journal of Modern Dynamics, 2013, 7 (4) : 527-552. - https://doi.org/10.3934/jmd.2013.7.527

  • BUZZI, Jérôme, FISHER, Tom, SAMBARINO, Martín, et al. Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems. Ergodic theory and dynamical systems, 2012, vol. 32, no 1, p. 63-79. - https://doi.org/10.1017/S0143385710000854

  • BOWEN, Rufus. Entropy-expansive maps. Transactions of the American Mathematical Society, 1972, vol. 164, p. 323-331. - https://doi.org/10.2307/1995978

  • BOWEN, Rufus. Some systems with unique equilibrium states. Theory of computing systems, 1974, vol. 8, no 3, p. 193-202. - https://doi.org/10.1007/BF01762666

  • BONATTI, Christian et VIANA, Marcelo. SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Israel Journal of Mathematics, 2000, vol. 115, no 1, p. 157-193. - https://doi.org/10.1007/BF02810585

  • CLIMENHAGA, Vaughn, FISHER, Todd, et THOMPSON, Daniel J. Unique equilibrium states for Bonatti–Viana diffeomorphisms. Nonlinearity, 2018, vol. 31, no 6, p. 2532. - https://doi.org/10.1088/1361-6544/aab1cd

  • CLIMENHAGA, Vaughn, FISHER, Todd, et THOMPSON, Daniel J. Equilibrium states for Mané diffeomorphisms. Ergodic Theory and Dynamical Systems, 2018, p. 1-23. - https://doi.org/10.1017/etds.2017.125

  • CLIMENHAGA, Vaughn et THOMPSON, Daniel J. Intrinsic ergodicity via obstruction entropies. Ergodic Theory and Dynamical Systems, 2014, vol. 34, no 6, p. 1816-1831. - https://doi.org/10.1017/etds.2013.16

  • CLIMENHAGA, Vaughn et THOMPSON, Daniel J. Unique equilibrium states for flows and homeomorphisms with non-uniform structure. Advances in Mathematics, 2016, vol. 303, p. 745-799. - https://doi.org/10.1016/j.aim.2016.07.029

  • COWIESON, William et YOUNG, Lai-Sang. SRB measures as zero-noise limits. Ergodic Theory and dynamical systems, 2005, vol. 25, no 4, p. 1115-1138. - https://doi.org/10.1017/S0143385704000604

  • KATOK, Anatole. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publications Mathématiques de l'IHÉS, 1980, vol. 51, p. 137-173. - https://doi.org/10.1007/BF02684777

  • MAÑÉ, Ricardo. Contributions to the stability conjecture. Topology, 1978, vol. 17, no 4, p. 383-396. - https://doi.org/10.1016/0040-9383(78)90005-8

  • URES, Raúl. Intrinsic ergodicity of partially hyperbolic diffeomorphisms with a hyperbolic linear part. Proceedings of the American Mathematical Society, 2012, vol. 140, no 6, p. 1973-1985. - https://doi.org/10.1090/S0002-9939-2011-11040-2

  • WALTERS, Peter. An introduction to ergodic theory. Graduate Texts in Mathematics, 1982, vol. 79. -


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