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Closed geodesics and the measure of maximal entropy on surfaces without conjugate points
Multi angle
Authors : Climenhaga, Vaughn (Author of the conference)
CIRM (Publisher )
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 - Geodesic flows
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/01/2020 Conference Date : 10/12/2019 Subseries : Research talks arXiv category : Dynamical Systems ; Differential Geometry Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:42:31 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-12-10_Climenhaga.mp4 
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Information on the Event
Event Title : 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 applicationsEvent Organizers : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro Dates : 09/12/2019 - 13/12/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2109.html
Citation Data
DOI : 10.24350/CIRM.V.19586603Cite this video as: 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 |
See Also
- [Multi angle] Besov spaces in multifractal environment, and the Frisch-Parisi conjecture / Author of the conference Seuret, Stéphane.
- [Multi angle] Marked length spectrum rigidity and the geodesic stretch / Author of the conference Knieper, Gerhard.
- [Multi angle] Intermediate dimensions, capacities and projections / Author of the conference Falconer, Kenneth.
- [Post-edited] Emergence of wandering stable components / Author of the conference Berger, Pierre.
Bibliography
- 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
