CIRM - Videos & books Library - Beyond Bowen specification property

Multi angle

Authors : Climenhaga, Vaughn (Author of the conference)
CIRM (Publisher )

Loading the player...

Abstract : 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

MSC Codes :
37B10 - Symbolic dynamics
37B40 - Topological entropy
37D35 - Thermodynamic formalism, variational principles, equilibrium states

Additional resources :
https://www.cirm-math.fr/RepOrga/1947/Notes/Climenhaga-2-notes.pdf

Information on the Video

Film maker :

Recanzone, Luca

Language :

Available date :

Conference Date :

Subseries :

arXiv category :

Mathematical Area(s) :

Format :

Video Time :

Targeted Audience :

Download :

https://videos.cirm-math.fr/2019-05-15_Climenhaga_Part2.mp4

Information on the Event

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

Citation Data

DOI : 10.24350/CIRM.V.19525203
Cite this video as: 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

[Multi angle] Ergodic optimization - lecture 3 / Author of the conference Contreras, Gonzalo.
[Multi angle] Ergodic optimization - lecture 2 / Author of the conference Contreras, Gonzalo.
[Multi angle] Ergodic optimization - lecture 1 / Author of the conference Contreras, Gonzalo.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 3 / Author of the conference Burguet, David.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2 / Author of the conference Burguet, David.
[Multi angle] Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 1 / Author of the conference Burguet, David.
[Multi angle] Rigidity in rank one: dynamics and geometry - lecture 3 / Author of the conference Gogolev, Andrey.
[Multi angle] Rigidity in rank one: dynamics and geometry - lecture 2 / Author of the conference Gogolev, Andrey.
[Multi angle] Rigidity in rank one: dynamics and geometry - lecture 1 / Author of the conference Gogolev, Andrey.
[Multi angle] Big mapping class groups - lecture 5 / Author of the conference Calegari, Danny.
[Multi angle] Big mapping class groups - lecture 4 / Author of the conference Calegari, Danny.
[Multi angle] Big mapping class groups - lecture 3 / Author of the conference Calegari, Danny.
[Multi angle] Big mapping class groups - lecture 2 / Author of the conference Calegari, Danny.
[Multi angle] Big mapping class groups - lecture 1 / Author of the conference Calegari, Danny.
[Multi angle] Beyond Bowen specification property - lecture 3 / Author of the conference Thompson, Daniel J..
[Multi angle] Beyond Bowen specification property - lecture 2 / Author of the conference Thompson, Daniel J..
[Multi angle] Beyond Bowen specification property - lecture 1 / Author of the conference Thompson, Daniel J..
[Multi angle] Beyond Bowen specification property - lecture 3 / Author of the conference Climenhaga, Vaughn.
[Multi angle] Beyond Bowen specification property - lecture 1 / Author of the conference Climenhaga, Vaughn.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 3 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 2 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 1 / Author of the conference Varju, Peter.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 3 / Author of the conference Shmerkin, Pablo.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 2 / Author of the conference Shmerkin, Pablo.
[Multi angle] Additive combinatorics methods in fractal geometry - lecture 1 / Author of the conference Shmerkin, Pablo.
[Multi angle] Transfer operators for Anosov flows - lecture 3 / Author of the conference Tsuijii, Masato.
[Multi angle] Transfer operators for Anosov flows - lecture 2 / Author of the conference Tsuijii, Masato.
[Multi angle] Transfer operators for Anosov flows - lecture 1 / Author of the conference Tsuijii, Masato.
[Multi angle] Transfer operators for Sinai billiards - lecture 3 / Author of the conference Baladi, Viviane.
[Multi angle] Transfer operators for Sinai billiards - lecture 2 / Author of the conference Baladi, Viviane.
[Multi angle] Transfer operators for Sinai billiards - lecture 1 / Author of the conference Baladi, Viviane.

Bibliography

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. -

Climenhaga2.jpg

Bookmarks Report an error

TRUSTEES

INSTITUTIONAL PARTNERS

Destination de la recherche

Raccourcis

See Also