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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