Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1 | Vidéo

Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1

Appears in collection : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discrets

In these lectures, we are interested in the chaotic behaviour of the geodesic flow of hyperbolic surfaces. To understand it from an ergodic point of view, we will build a family of invariant measures called "Gibbs measures", and use their product structure to deduce chaotic properties of the flow. We will also present some situations where this family of measures leads to nice geometric results.

Information about the video

Date of recording 15/04/2025
Date of publication 25/04/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20342603
Cite this video Schapira, Barbara (15/04/2025). Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20342603
URL https://dx.doi.org/10.24350/CIRM.V.20342603

Domain(s)

Bibliography

PAULIN, Frédéric, POLLICOTT, Mark, et SCHAPIRA, Barbara. Equilibrium states in negative curvature. Asterisque n°373, 2012. - http://doi.org/10.24033/ast.975
SCHAPIRA, Barbara et TAPIE, Samuel. Regularity of entropy, geodesic currents and entropy at infinity. arXiv preprint arXiv:1802.04991, 2018. - https://doi.org/10.48550/arXiv.1802.04991
LEDRAPPIER, François. Structure au bord des variétés à courbure négative. Séminaire de théorie spectrale et géométrie, 1994, vol. 13, p. 97-122. - https://www.numdam.org/item/TSG_1994-1995__13__97_0.pdf