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Unique ergodicity of geodesic flow in an infinite translation surface
Multi angle
Authors : Rafi, Kasra (Author of the conference)
CIRM (Publisher )
37A25 - Ergodicity, mixing, rates of mixing
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
51A40 - Translation planes and spreads
CIRM (Publisher )
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Abstract :
The behaviour of infinite translation surfaces is, in many regards, very different from the finite case. For example, the geodesic flow is often not recurrent or is not even defined for infinite time in a generic direction.
However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is uniquely ergodic in almost every direction. We call this class of surface essentially finite.
(joint work with Anja Randecker).
MSC Codes : However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is uniquely ergodic in almost every direction. We call this class of surface essentially finite.
(joint work with Anja Randecker).
37A25 - Ergodicity, mixing, rates of mixing
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
51A40 - Translation planes and spreads
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/02/2017 Conference Date : 14/02/2017 Subseries : Research talks arXiv category : Group Theory ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:59:39 Download : https://videos.cirm-math.fr/2017-02-14_Rafi.mp4 
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Information on the Event
Event Title : Teichmüller Space, Polygonal Billiard, Interval Exchanges / Espace de Teichmüller. Billards polygonaux, échanges d'intervallesEvent Organizers : Chaika, Jon ; Hubert, Pascal ; Lanneau, Erwan ; Skripchenko, Alexandra ; Zorich, Anton Dates : 13/02/2017 - 17/02/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1713.html
Citation Data
DOI : 10.24350/CIRM.V.19119803Cite this video as: Rafi, Kasra (2017). Unique ergodicity of geodesic flow in an infinite translation surface . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19119803 URI : http://dx.doi.org/10.24350/CIRM.V.19119803 |
See Also
- [Multi angle] Simplicity of the Lyapunov spectrum revisited / Author of the conference Hamenstädt, Ursula.
- [Multi angle] Limits of geodesic push-forwards of horocycle measures / Author of the conference Forni, Giovanni.
- [Multi angle] Interval exchange transformations from tiling billiards / Author of the conference Davis, Diana.
- [Post-edited] Totally geodesic submanifolds of Teichmüller space and moduli space / Author of the conference Wright, Alexander.
Bibliography
