中心对称八角形的五角形刚性

Pub Date : 2024-04-02 DOI:10.1093/imrn/rnae050

Richard Evan Schwartz

{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae050\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我将建立一个猜想的特例，这个猜想将深对角五角星映射和庞斯莱多边形交织在一起。这个特例是作用于中心对称八角形的仿射等价类上的 3 美元对角线映射。证明过程包括确定该映射在这种情况下是阿诺德-利乌维尔可积分的，然后详细探讨拉格朗日曲面折叠。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助