Closed geodesics and the measure of maximal entropy on surfaces without conjugate points | Vidéo | Carmin.tv

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Closed geodesics and the measure of maximal entropy on surfaces without conjugate points

By Vaughn Climenhaga

Appears in collection : 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 applications

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.

Information about the video

Date of recording 10/12/2019
Date of publication 23/01/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19586603
Cite this video Climenhaga, Vaughn (10/12/2019). Closed geodesics and the measure of maximal entropy on surfaces without conjugate points. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19586603
URL https://dx.doi.org/10.24350/CIRM.V.19586603

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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

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