{"title":"神奇的台球：椭圆边界案例","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":"{\"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}","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}
Magic Billiards: the Case of Elliptical Boundaries
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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