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Anosov flows in 3 dimensions and Anosov-like actions - Part 1
Multi angle
Authors : Mann, Kathryn (Author of the conference) ; Barthelmé, Thomas (Author of the conference)
CIRM (Publisher )
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37C10 - Vector fields, flows, ordinary differential equations
37C27 - periodic orbits of vector fields and flows
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
57S25 - Groups acting on specific manifolds
CIRM (Publisher )
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Abstract :
A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.
Keywords : Anosov flow; pseudo-Anosov flow; Anosov-like action; bifoliated plane
MSC Codes : Keywords : Anosov flow; pseudo-Anosov flow; Anosov-like action; bifoliated plane
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37C10 - Vector fields, flows, ordinary differential equations
37C27 - periodic orbits of vector fields and flows
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
57S25 - Groups acting on specific manifolds
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/05/2023 Conference Date : 10/04/2023 Subseries : Research School arXiv category : Dynamical Systems ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:02:55 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-04-10_Barthelme_1.mp4 
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Information on the Event
Event Title : Anosov Dynamics / La dynamique des sytèmes d'AnosovEvent Organizers : Barbot, Thierry ; Barthelmé, Thomas ; Foulon, Patrick ; Hasselblatt, Boris ; Rechtman, Ana Dates : 10/04/2023 - 14/04/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2753.html
Citation Data
DOI : 10.24350/CIRM.V.20036303Cite this video as: Mann, Kathryn ;Barthelmé, Thomas (2023). Anosov flows in 3 dimensions and Anosov-like actions - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20036303 URI : http://dx.doi.org/10.24350/CIRM.V.20036303 |
See Also
- [Multi angle] Contact flows and Birkhoff sections - Part 3 / Author of the conference Vaugon, Anne ; Author of the conference Dehornoy, Pierre.
- [Multi angle] Anosov flows in 3 dimensions and Anosov-like actions - Part 3 / Author of the conference Mann, Kathryn ; Author of the conference Barthelmé, Thomas.
- [Multi angle] Microlocal methods for Anosov flows - Part 3 / Author of the conference Guillarmou, Colin.
- [Multi angle] Microlocal methods for Anosov flows - Part 2 / Author of the conference Guillarmou, Colin.
- [Multi angle] Contact flows and Birkhoff sections - Part 1 / Author of the conference Vaugon, Anne ; Author of the conference Dehornoy, Pierre.
- [Multi angle] Microlocal methods for Anosov flows - Part 1 / Author of the conference Guillarmou, Colin.
- [Multi angle] Anosov flows in 3 dimensions and Anosov-like actions - Part 2 / Author of the conference Mann, Kathryn ; Author of the conference Barthelmé, Thomas.
- [Multi angle] Contact flows and Birkhoff sections - Part 2 / Author of the conference Vaugon, Anne ; Author of the conference Dehornoy, Pierre.
Bibliography
- BARTHELMÉ, Thomas, FRANKEL, Steven, et MANN, Kathryn. Orbit equivalences of pseudo-Anosov flows. arXiv preprint arXiv:2211.10505, 2022. - https://doi.org/10.48550/arXiv.2211.10505
- BARTHELMÉ, Thomas et MANN, Kathryn. Orbit equivalences of $\mathbb {R} $-covered Anosov flows and applications. arXiv preprint arXiv:2012.11811, 2020. - https://doi.org/10.48550/arXiv.2012.11811
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