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Billiards on regular polygons
Multi angle
Authors : Davis, Diana (Author of the conference)
CIRM (Publisher )
37D50 - Hyperbolic systems with singularities (billiards, etc.)
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
37E35 - Flows on surfaces
CIRM (Publisher )
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Abstract :
Periodic trajectories in polygons are rare and beautiful, and have several surprising properties. During the lockdown period in 2020, we wrote a Sage program to draw every periodic trajectory on every regular polygon with an odd number of edges. I'll explain the underlying structure, and show lots of pictures from this vast menagerie. This is joint work with Samuel Lelièvre.
Keywords : periodic; billiards; regular polygon; Euclidean algorithm
MSC Codes : Keywords : periodic; billiards; regular polygon; Euclidean algorithm
37D50 - Hyperbolic systems with singularities (billiards, etc.)
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
37E35 - Flows on surfaces
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/11/2021 Conference Date : 04/10/2021 Subseries : Research talks arXiv category : Dynamical Systems ; Electrical Engineering and Systems Science Mathematical Area(s) : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:50:56 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-10-04_Davis.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.19820003Cite this video as: Davis, Diana (2021). Billiards on regular polygons. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19820003 URI : http://dx.doi.org/10.24350/CIRM.V.19820003 |
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] Degenerate billiards / Author of the conference Bolotin, Sergei.
- [Multi angle] Birkhoff-Poritsky conjecture for centrally-symmetric billiards / Author of the conference Bialy, Michael.
Bibliography
- DAVIS, Diana et LELIEVRE, Samuel. Periodic paths on the pentagon, double pentagon and golden L. arXiv preprint arXiv:1810.11310, 2018. - https://arxiv.org/abs/1810.11310
- MCMULLEN, Curtis T. Modular symbols for Teichmüller curves. Journal für die reine und angewandte Mathematik, 2021. - https://doi.org/10.1515/crelle-2021-0019
