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Geodesic flow on surfaces without conjugate points - part 2

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Auteurs : War, Khadim Mbacke (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : The aim of this lecture series is to study some ergodic properties of the geodesic flow on surfaces without conjugate points. In the first two lectures we give an introduction the geodesic flow and discuss the geometric properties of the surface that are needed to study,this includes the action of the fundamental group on the universal cover, the Gromov boundary and Morse Lemma. In the third lecture we will introduce the Poincaré series and define the measure of maximal entropy via Patterson-Sullivan construction. In the fourth lecture, we will show that the measure of maximal entropy is unique and we will use the cross ratio function to prove the geodesic flow is mixing with respect to the constructed measure. In the last lecture, we will prove the prime geodesic theorem of the surface. This is based on two joint work with Gerhard Knieper and Vaughn Climenhaga.

Codes MSC :
37C35 - orbit growth
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53C22 - Geodesics [See also 58E10]

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Français
    Date de publication : 06/09/2024
    Date de captation : 23/07/2024
    Sous collection : Research School
    arXiv category : Dynamical Systems ; Differential Geometry
    Domaine : Dynamical Systems & ODE ; Geometry
    Format : MP4 (.mp4) - HD
    Durée : 01:30:52
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-07-23_War_Part_2.mp4

Informations sur la Rencontre

Nom de la rencontre : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfaces
Organisateurs de la rencontre : Gaye, Masseye ; Quint, Jean-François
Dates : 22/07/2024 - 26/07/2024
Année de la rencontre : 2024
URL Congrès : https://conferences.cirm-math.fr/3294.html

Données de citation

DOI : 10.24350/CIRM.V.20207703
Citer cette vidéo: War, Khadim Mbacke (2024). Geodesic flow on surfaces without conjugate points - part 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20207703
URI : http://dx.doi.org/10.24350/CIRM.V.20207703

Voir aussi

Bibliographie

  • CLIMENHAGA, Vaughn, KNIEPER, Gerhard, et WAR, Khadim. Closed geodesics on surfaces without conjugate points. Communications in Contemporary Mathematics, 2022, vol. 24, no 06, p. 2150067. - https://doi.org/10.1142/S021919972150067X

  • CLIMENHAGA, Vaughn, KNIEPER, Gerhard, et WAR, Khadim. Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points. Advances in Mathematics, 2021, vol. 376, p. 107452. - https://doi.org/10.1016/j.aim.2020.107452



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