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Generic properties of the geodesic flow in nonpositive curvature
Multi angle
Authors : Coudène, Yves (Author of the conference)
CIRM (Publisher )
34C28 - Complex behavior, chaotic systems (ODE)
37B10 - Symbolic dynamics
37C20 - Generic properties, structural stability
37C40 - Smooth ergodic theory, invariant measures
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
CIRM (Publisher )
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Abstract :
I will survey recent results on the generic properties of probability measures invariant by the geodesic flow defined on a nonpositively curved manifold. Such a flow is one of the early example of a non-uniformly hyperbolic system. I will talk about ergodicity and mixing both in the compact and noncompact setting, and ask some questions about the associated frame flow, which is partially hyperbolic.
MSC Codes : 34C28 - Complex behavior, chaotic systems (ODE)
37B10 - Symbolic dynamics
37C20 - Generic properties, structural stability
37C40 - Smooth ergodic theory, invariant measures
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/03/2017 Conference Date : 21/02/17 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:50:33 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-02-21_Coudene.mp4 
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Information on the Event
Event Title : Non uniformly hyperbolic dynamical systems. Coupling and renewal theory / Systèmes dynamiques non uniformement et partiellement hyperboliques. Couplage, renouvellementEvent Organizers : Troubetzkoy, Serge ; Vaienti, Sandro Dates : 20/02/17 - 24/02/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1714.html
Citation Data
DOI : 10.24350/CIRM.V.19128803Cite this video as: Coudène, Yves (2017). Generic properties of the geodesic flow in nonpositive curvature. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19128803 URI : http://dx.doi.org/10.24350/CIRM.V.19128803 |
See Also
- [Multi angle] Fast-Slow partially hyperbolic systems: an example / Author of the conference Liverani, Carlangelo.
- [Multi angle] Mixing and rates of mixing for infinite measure flows / Author of the conference Melbourne, Ian.
- [Multi angle] Central limit theorems for circle packings / Author of the conference Pollicott, Mark.
- [Post-edited] Singular hyperbolicity and homoclinic tangencies of 3-dimensional flows / Author of the conference Crovisier, Sylvain.
Bibliography
- Coudène, Y., & Schapira, B. (2014). Generic measures for geodesic flows on nonpositively curved manifolds. Journal de l'École Polytechnique – Mathématiques, 1, 387-408 - http://dx.doi.org/10.5802/jep.14
- Coudène, Y., & Schapira, . (2011). Counterexamples in non-positive curvature. Discrete and Continuous Dynamical Systems - Series A, 30 (4),1095–1106 - http://dx.doi.org/10.3934/dcds.2011.30.1095
- Coudene, Y. (2003). Gibbs measures on negatively curved manifolds.
Journal of Dynamical and Control Systems, 9 (1), 89–101 - http://dx.doi.org/10.1023/A:1022107301618
