English
Closed geodesics and the measure of maximal entropy on surfaces without conjugate points
Multi angle
Auteurs : Climenhaga, Vaughn (Auteur de la Conférence)
CIRM (Editeur )
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 - Geodesic flows
CIRM (Editeur )
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Résumé :
For negatively curved Riemannian manifolds, Margulis gave an asymptotic formula for the number of closed geodesics with length below a given threshold. I will describe joint work with Gerhard Knieper and Khadim War in which we obtain the corresponding result for surfaces without conjugate points by first proving uniqueness of the measure of maximal entropy and then following the approach of recent work by Russell Ricks, who established the asymptotic estimates in the setting of CAT(0) geodesic flows.
Keywords : closed geodesics; noconjugate points
Codes MSC : Keywords : closed geodesics; noconjugate points
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 - Geodesic flows
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 23/01/2020 Date de captation : 10/12/2019 Sous collection : Research talks arXiv category : Dynamical Systems ; Differential Geometry Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:42:31 Audience : Researchers Download : https://videos.cirm-math.fr/2019-12-10_Climenhaga.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2019 - Conference - Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications / Chaire Jean-Morlet 2019 - Conférence - Formalisme thermodynamique : systèmes dynamiques, propriétés statistiques et leurs applicationsOrganisateurs de la rencontre : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro Dates : 09/12/2019 - 13/12/2019 Année de la rencontre : 2019 URL Congrès : https://www.chairejeanmorlet.com/2109.html
Données de citation
DOI : 10.24350/CIRM.V.19586603Citer cette vidéo: Climenhaga, Vaughn (2019). Closed geodesics and the measure of maximal entropy on surfaces without conjugate points. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586603 URI : http://dx.doi.org/10.24350/CIRM.V.19586603 |
Voir aussi
- [Multi angle] Besov spaces in multifractal environment, and the Frisch-Parisi conjecture / Auteur de la Conférence Seuret, Stéphane.
- [Multi angle] Marked length spectrum rigidity and the geodesic stretch / Auteur de la Conférence Knieper, Gerhard.
- [Multi angle] Intermediate dimensions, capacities and projections / Auteur de la Conférence Falconer, Kenneth.
- [ Post-edited] Emergence of wandering stable components / Auteur de la Conférence Berger, Pierre.
Bibliographie
- CLIMENHAGA, Vaughn, KNIEPER, Gerhard, et WAR, Khadim. Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points. arXiv preprint arXiv:1903.09831, 2019. - https://arxiv.org/abs/1903.09831
