Français
Geodesic flow on surfaces without conjugate points - part 1
Multi angle
Authors : War, Khadim Mbacke (Author of the conference)
CIRM (Publisher )
37C35 - orbit growth
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53C22 - Geodesics [See also 58E10]
CIRM (Publisher )
Loading the player...
|
Abstract :
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.
MSC Codes : 37C35 - orbit growth
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53C22 - Geodesics [See also 58E10]
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : French Available date : 06/09/2024 Conference Date : 22/07/2024 Subseries : Research School arXiv category : Dynamical Systems ; Differential Geometry Mathematical Area(s) : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Video Time : 01:30:18 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-07-22_War_Part_1.mp4 
|
Information on the Event
Event Title : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfacesEvent Organizers : Gaye, Masseye ; Quint, Jean-François Dates : 22/07/2024 - 26/07/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3294.html
Citation Data
DOI : 10.24350/CIRM.V.20207303Cite this video as: 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 |
See Also
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 3 / Author of the conference Valdez, Ferrán.
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 2 / Author of the conference Valdez, Ferrán.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 3 / Author of the conference War, Khadim Mbacke.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 2 / Author of the conference War, Khadim Mbacke.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 3 / Author of the conference Lo, Cheikh.
- [Multi angle] Random walks on groups - part 3 / Author of the conference Aoun, Richard.
- [Multi angle] Random walks on groups - part 2 / Author of the conference Aoun, Richard.
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 1 / Author of the conference Valdez, Ferrán.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 1 / Author of the conference Lo, Cheikh.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 2 / Author of the conference Anonymous, A..
- [Multi angle] Random walks on groups - part 1 / Author of the conference Aoun, Richard.
Bibliography
- 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
Imagette Video
