Authors: | Dragović, Vladimir Radnović, Milena |
Affiliations: | Mechanics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Magic Billiards: the Case of Elliptical Boundaries | Issue Date: | 2024 | ISSN: | 2331-8422 | URL: | http://arxiv.org/abs/2409.03158v2 | Abstract: | In this work, we introduce a novel concept of magic billiards, which can be seen as an umbrella, unifying several well-known generalisations of mathematical billiards. We analyse properties of magic billiards in the case of elliptical boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic, and polynomial forms. A topological description of those billiards is given using Fomenko graphs. |
Description: | 19 pages, 14 figures |
Keywords: | Mathematics - Dynamical Systems; Mathematics - Dynamical Systems; Nonlinear Sciences - Exactly Solvable and Integrable Systems; 37C83, 37J35, 37J39 | Publisher: | arXiv |
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