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Transfer operators for Sinai billiards - lecture 1

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Multi angle
Auteurs : Baladi, Viviane (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

Keywords : dynamical systems; billiards; transfer operators

Codes MSC :
37B40 - Topological entropy
 37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
 37D50 - Hyperbolic systems with singularities (billiards, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/1947/Notes/Baladi-notes.pdf
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 11/06/2019
    Date de captation : 16/05/2019
    Sous collection : Research School
    arXiv category : Dynamical Systems ; Spectral Theory ; Mathematical Physics
    Domaine : Dynamical Systems & ODE ; Analysis and its Applications
    Format : MP4 (.mp4) - HD
    Durée : 00:55:32
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-05-16_Baladi_part1.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.19523703
Citer cette vidéo: Baladi, Viviane (2019). Transfer operators for Sinai billiards - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19523703
URI : http://dx.doi.org/10.24350/CIRM.V.19523703

Voir aussi

Bibliographie

  • BALADI, Viviane et DEMERS, Mark. On the Measure of Maximal Entropy for Finite Horizon Sinai Billiard Maps. arXiv preprint arXiv:1807.02330, 2018. - https://arxiv.org/abs/1807.02330

  • BALADI, Viviane, DEMERS, Mark F., et LIVERANI, Carlangelo. Exponential decay of correlations for finite horizon Sinai billiard flows. Inventiones mathematicae, 2018, vol. 211, no 1, p. 39-177. - https://doi.org/10.1007/s00222-017-0745-1

  • BOWEN, Rufus. Topological entropy for noncompact sets. Transactions of the American Mathematical Society, 1973, vol. 184, p. 125-136. - https://doi.org/10.2307/1996403

  • BOWEN, Rufus. Maximizing entropy for a hyperbolic flow. Theory of Computing Systems, 1973, vol. 7, no 3, p. 300-303. - https://doi.org/10.1007/BF01795948

  • BRIN, Michael et KATOK, Anatole. On local entropy. In : Geometric dynamics. Springer, Berlin, Heidelberg, 1983. p. 30-38. - https://doi.org/10.1007/BFb0061408

  • BUNIMOVICH, Leonid Abramovich, SINAI, Yakov G., et CHERNOV, Nikolai Ivanovich. Markov partitions for two-dimensional hyperbolic billiards. Russian Mathematical Surveys, 1990, vol. 45, no 3, p. 105. - https://doi.org/10.1070/RM1990v045n03ABEH002355

  • CHERNOV, Nikolai Ivanovich. Topological entropy and periodic points of two-dimensional hyperbolic billiards. Functional Analysis and Its Applications, 1991, vol. 25, no 1, p. 39-45. - https://doi.org/10.1007/BF01090675

  • CHERNOV, N. I. et MARKARIAN, R. Mathematical Surveys and Monographs. Chaotic Billiards, 2006, vol. 127. -

  • DEMERS, Mark F., WRIGHT, Paul, et YOUNG, Lai-Sang. Entropy, Lyapunov exponents and escape rates in open systems. Ergodic Theory and Dynamical Systems, 2012, vol. 32, no 4, p. 1270-1301. - https://doi.org/10.1017/S0143385711000344

  • DEMERS, Mark et ZHANG, Hong-Kun. Spectral analysis of the transfer operator for the Lorentz gas. Journal of Modern Dynamics, 2011, vol. 5, no 4. - https://doi.org/10.3934/jmd.2011.5.665

  • GOUËZEL, Sébastien, LIVERANI, Carlangelo, et al. Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties. Journal of Differential Geometry, 2008, vol. 79, no 3, p. 433-477. - https://arxiv.org/abs/math/0606722

  • LIMA, Yuri et MATHEUS, Carlos. Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities. arXiv preprint arXiv:1606.05863, 2016. - https://arxiv.org/abs/1606.05863

  • PESIN, Yakov B. Dimension theory in dynamical systems: contemporary views and applications. University of Chicago Press, 2008. -

  • PESIN, Ya B. et PITSKEL', B. S. Topological pressure and the variational principle for noncompact sets. Functional Analysis and its Applications, 1984, vol. 18, no 4, p. 307-318. - https://doi.org/10.1007/BF01083692

  • SINAI, Yakov G. Dynamical systems with elastic reflections. Russian Mathematical Surveys, 1970, vol. 25, no 2, p. 137. - https://doi.org/10.1070/RM1970v025n02ABEH003794

  • YOUNG, Lai-Sang. Statistical properties of dynamical systems with some hyperbolicity. Annals of Mathematics, 1998, vol. 147, p. 585-650. - https://doi.org/102307/120960


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