Transfer operators for Sinai billiards - lecture 1 | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Transfer operators for Sinai billiards - lecture 1

By Viviane Baladi

Appears in 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.

Information about the video

Date of recording 16/05/2019
Date of publication 11/06/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19523703
Cite this video Baladi, Viviane (16/05/2019). Transfer operators for Sinai billiards - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19523703
URL https://dx.doi.org/10.24350/CIRM.V.19523703

Domain(s)

Bibliography

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

MSC codes

Document(s)

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

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2026

Give feedback