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Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1
Multi angle
Authors : Schapira, Barbara (Author of the conference)
CIRM (Publisher )
37A35 - Entropy and other invariants, isomorphism, classification
37B40 - Topological entropy
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A10 - One-parameter continuous families of measure-preserving transformations
37A40 - Nonsingular (and infinite-measure preserving) transformations
CIRM (Publisher )
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Abstract :
In these lectures, we are interested in the chaotic behaviour of the geodesic flow of hyperbolic surfaces. To understand it from an ergodic point of view, we will build a family of invariant measures called "Gibbs measures", and use their product structure to deduce chaotic properties of the flow. We will also present some situations where this family of measures leads to nice geometric results.
Keywords : geodesic flow; negative curvature; thermodynamical formalism
MSC Codes : Keywords : geodesic flow; negative curvature; thermodynamical formalism
37A35 - Entropy and other invariants, isomorphism, classification
37B40 - Topological entropy
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A10 - One-parameter continuous families of measure-preserving transformations
37A40 - Nonsingular (and infinite-measure preserving) transformations
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 25/04/2025 Conference Date : 15/04/2025 Subseries : Research School arXiv category : Dynamical Systems ; Differential Geometry Mathematical Area(s) : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Video Time : 01:32:03 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-15_Schapira_Part1 
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Information on the Event
Event Title : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discretsEvent Organizers : Bromberg, Kenneth ; Dal'Bo, Françoise ; Parreau, Anne ; Tholozan, Nicolas ; Toulisse, Jérémy Dates : 14/04/2025 - 18/04/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3241.html
Citation Data
DOI : 10.24350/CIRM.V.20342603Cite this video as: Schapira, Barbara (2025). Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20342603 URI : http://dx.doi.org/10.24350/CIRM.V.20342603 |
See Also
- [Multi angle] Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 2 / Author of the conference Schapira, Barbara.
- [Multi angle] Introduction to Teichmüller theory Lecture 2 / Author of the conference Fanoni, Federica.
- [Multi angle] Introduction to Teichmüller theory Lecture 1 / Author of the conference Fanoni, Federica.
Bibliography
- PAULIN, Frédéric, POLLICOTT, Mark, et SCHAPIRA, Barbara. Equilibrium states in negative curvature. Asterisque n°373, 2012. - http://doi.org/10.24033/ast.975
- SCHAPIRA, Barbara et TAPIE, Samuel. Regularity of entropy, geodesic currents and entropy at infinity. arXiv preprint arXiv:1802.04991, 2018. - https://doi.org/10.48550/arXiv.1802.04991
- LEDRAPPIER, François. Structure au bord des variétés à courbure négative. Séminaire de théorie spectrale et géométrie, 1994, vol. 13, p. 97-122. - https://www.numdam.org/item/TSG_1994-1995__13__97_0.pdf
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