| 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 | Journal: | Sbornik Mathematics | Issue Date: | 2025 | Rank: | M22 | ISSN: | 1064-5616 | DOI: | 10.4213/sm10181e | Abstract: | We introduce a novel concept of magic billiards, which can be viewed as an umbrella unifying several well-known generalisations of mathematical billiards. We analyse the properties of magic billiards in the case of elliptic boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic and polynomial forms. A topological description of these billiards is given using Fomenko graphs. |
Keywords: | elliptical billiards, topological billiards | Fomenko graphs | periodic trajectories | divisors on elliptic curves | polynomial Pell equations | Publisher: | Steklov Mathematical Institute of Russian Academy of Sciences | Project: | Mathematical Institute of the Serbian Academy of Sciences and Arts, the Science Fund of Serbia (grant MEGIC no. 7744592 “Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics”) and the Ministry of Education, Science, and Technological Development of the Republic of Serbia. The research of V. Dragović was also supported by the Simons Foundation (grant no. 854861). |
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