{"title":"探索椭圆台球中的自交n周期","authors":"Ronaldo Garcia, D. Reznik","doi":"10.33039/ami.2022.02.001","DOIUrl":null,"url":null,"abstract":"This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exploring self-intersected N-periodics in the elliptic billiard\",\"authors\":\"Ronaldo Garcia, D. Reznik\",\"doi\":\"10.33039/ami.2022.02.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.\",\"PeriodicalId\":43454,\"journal\":{\"name\":\"Annales Mathematicae et Informaticae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematicae et Informaticae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33039/ami.2022.02.001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2022.02.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Exploring self-intersected N-periodics in the elliptic billiard
This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.
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