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H 1 Closed geodesics and the measure of maximal entropy on surfaces without conjugate points

Auteurs : Climenhaga, Vaughn (Auteur de la Conférence)
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 :
    37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
    53D25 - Geodesic flows

    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 applications
    Organisateurs 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/2019-2-...

    Citation Data

    DOI : 10.24350/CIRM.V.19586603
    Cite 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

    Voir aussi


    1. 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