{"title":"Magic Billiards: the Case of Elliptical Boundaries","authors":"Vladimir Dragović, Milena Radnović","doi":"arxiv-2409.03158","DOIUrl":null,"url":null,"abstract":"In this work, we introduce a novel concept of magic billiard games and\nanalyse their properties in the case of elliptical boundaries. We provide\nexplicit conditions for periodicity in algebro-geometric, analytic, and\npolynomial forms. A topological description of those billiards is given using\nFomenko graphs.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03158","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we introduce a novel concept of magic billiard games and
analyse their properties 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.
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