Magic billiards: the case of elliptic boundaries

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-geomet...

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Bibliographic Details
Published inSbornik. Mathematics Vol. 216; no. 5; pp. 654 - 673
Main Authors Dragovic, Vladimir Il'ich, Radnovic, Milena
Format Journal Article
LanguageEnglish
Published 2025
Online AccessGet full text
ISSN1064-5616
1468-4802
DOI10.4213/sm10181e

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Summary: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. Bibliography: 45 titles.
ISSN:1064-5616
1468-4802
DOI:10.4213/sm10181e