Français
Degenerate billiards
Multi angle
Authors : Bolotin, Sergei (Author of the conference)
CIRM (Publisher )
37D05 - Hyberbolic orbits and sets
37D50 - Hyperbolic systems with singularities (billiards, etc.)
37J10 - Symplectic mappings - Fixed points
70F16
CIRM (Publisher )
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Abstract :
In an ordinary billiard trajectories of a Hamiltonian system are reflected after a collision with a hypersurface (scatterer). If the scatterer has codimension more than one, we say that the billiard is degenerate. Degenerate billiards appear e.g. as limits of systems with singularities in celestial mechanics. We discuss the existence of trajectories of such systems shadowing trajectories of a degenerate billiard.
MSC Codes : 37D05 - Hyberbolic orbits and sets
37D50 - Hyperbolic systems with singularities (billiards, etc.)
37J10 - Symplectic mappings - Fixed points
70F16
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/11/2021 Conference Date : 07/10/2021 Subseries : Research talks arXiv category : Dynamical Systems ; Electrical Engineering and Systems Science Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:00:48 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-10-07_Bolotin.mp4 
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Information on the Event
Event Title : Differential Geometry, Billiards, and Geometric Optics / Géométrie différentielle, billards et optique géométriqueEvent Organizers : Glutsyuk, Alexey ; Izmestiev, Ivan ; Radnovic, Milena ; Tabachnikov, Sergei Dates : 04/10/2021 - 08/10/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2383.html
Citation Data
DOI : 10.24350/CIRM.V.19819903Cite this video as: Bolotin, Sergei (2021). Degenerate billiards. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19819903 URI : http://dx.doi.org/10.24350/CIRM.V.19819903 |
See Also
- [Multi angle] Geodesic scattering on hyperboloids / Author of the conference Veselov, Alexander.
- [Multi angle] Novikov's problem and tiling billiards / Author of the conference Paris-Romaskevich, Olga.
- [Multi angle] Billiards on regular polygons / Author of the conference Davis, Diana.
- [Multi angle] Birkhoff-Poritsky conjecture for centrally-symmetric billiards / Author of the conference Bialy, Michael.
Bibliography
- BOLOTIN, Sergey V. Degenerate billiards. Proceedings of the Steklov Institute of Mathematics, 2016, vol. 295, no 1, p. 45-62. - https://doi.org/10.1134/S0081543816080046
- BOLOTIN, Sergey V. Degenerate billiards in celestial mechanics. Regular and Chaotic Dynamics, 2017, vol. 22, no 1, p. 27-53. - https://arxiv.org/abs/1612.08907
