English
Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1
Multi angle
Auteurs : Schapira, Barbara (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Récanzone, LucaLangue : Anglais Date de publication : 25/04/2025 Date de captation : 15/04/2025 Sous collection : Research School arXiv category : Dynamical Systems ; Differential Geometry Domaine : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Durée : 01:32:03 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-15_Schapira_Part1 
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Informations sur la Rencontre
Nom de la rencontre : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discretsOrganisateurs de la rencontre : Bromberg, Kenneth ; Dal'Bo, Françoise ; Parreau, Anne ; Tholozan, Nicolas ; Toulisse, Jérémy Dates : 14/04/2025 - 18/04/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3241.html
Données de citation
DOI : 10.24350/CIRM.V.20342603Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 2 / Auteur de la Conférence Schapira, Barbara.
- [Multi angle] Introduction to Teichmüller theory Lecture 2 / Auteur de la Conférence Fanoni, Federica.
- [Multi angle] Introduction to Teichmüller theory Lecture 1 / Auteur de la Conférence Fanoni, Federica.
Bibliographie
- 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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