Transfer operators for Sinai billiards - lecture 3 | Vidéo | Carmin.tv

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Transfer operators for Sinai billiards - lecture 3

De Viviane Baladi

Apparaît dans la collection : Dynamique au-delà de l’hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity

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.

Informations sur la vidéo

Date de captation 17/05/2019
Date de publication 11/06/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19523903
Citer cette vidéo Baladi, Viviane (17/05/2019). Transfer operators for Sinai billiards - lecture 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19523903
URL https://dx.doi.org/10.24350/CIRM.V.19523903

Domaine(s)

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
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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

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/1947/Notes/Baladi-notes.pdf

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