{"title":"中心对称八角形的五角形刚性","authors":"Richard Evan Schwartz","doi":"10.1093/imrn/rnae050","DOIUrl":null,"url":null,"abstract":"In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pentagram Rigidity for Centrally Symmetric Octagons\",\"authors\":\"Richard Evan Schwartz\",\"doi\":\"10.1093/imrn/rnae050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.\",\"PeriodicalId\":14461,\"journal\":{\"name\":\"International Mathematics Research Notices\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematics Research Notices\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae050\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematics Research Notices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae050","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Pentagram Rigidity for Centrally Symmetric Octagons
In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.
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International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
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