English
Geodesic flow on surfaces without conjugate points - part 1
Multi angle
Auteurs : War, Khadim Mbacke (Auteur de la Conférence)
CIRM (Editeur )
37C35 - orbit growth
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53C22 - Geodesics [See also 58E10]
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]
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Français Date de publication : 06/09/2024 Date de captation : 22/07/2024 Sous collection : Research School arXiv category : Dynamical Systems ; Differential Geometry Domaine : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Durée : 01:30:18 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-07-22_War_Part_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfacesOrganisateurs 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.20207303Citer cette vidéo: War, Khadim Mbacke (2024). Geodesic flow on surfaces without conjugate points - part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20207303 URI : http://dx.doi.org/10.24350/CIRM.V.20207303 |
Voir aussi
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 3 / Auteur de la Conférence Valdez, Ferrán.
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 2 / Auteur de la Conférence Valdez, Ferrán.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 3 / Auteur de la Conférence War, Khadim Mbacke.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 2 / Auteur de la Conférence War, Khadim Mbacke.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 3 / Auteur de la Conférence Lo, Cheikh.
- [Multi angle] Random walks on groups - part 3 / Auteur de la Conférence Aoun, Richard.
- [Multi angle] Random walks on groups - part 2 / Auteur de la Conférence Aoun, Richard.
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 1 / Auteur de la Conférence Valdez, Ferrán.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 1 / Auteur de la Conférence Lo, Cheikh.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 2 / Auteur de la Conférence Anonymous, A..
- [Multi angle] Random walks on groups - part 1 / Auteur de la Conférence Aoun, Richard.
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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