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Geodesic flow on surfaces without conjugate points - part 3

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Authors : War, Khadim Mbacke (Author of the conference)
CIRM (Publisher )

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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, Guillaume
    Language : French
    Available date : 06/09/2024
    Conference Date : 25/07/2024
    Subseries : Research School
    arXiv category : Dynamical Systems ; Differential Geometry
    Mathematical Area(s) : Dynamical Systems & ODE ; Geometry
    Format : MP4 (.mp4) - HD
    Video Time : 01:27:34
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-07-25_War_Part_3.mp4

Information on the Event

Event Title : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfaces
Event 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.20207803
Cite this video as: War, Khadim Mbacke (2024). Geodesic flow on surfaces without conjugate points - part 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20207803
URI : http://dx.doi.org/10.24350/CIRM.V.20207803

See Also

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



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