有[数学]的魏格登曲面上的闭合大地线

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-07-03 DOI:10.1137/23m1608616

Frank E. Baginski, Valério Ramos Batista

{"title":"有[数学]的魏格登曲面上的闭合大地线","authors":"Frank E. Baginski, Valério Ramos Batista","doi":"10.1137/23m1608616","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1705-1719, September 2024. <br/> Abstract.In 2006, Alexander proved a result that implies for a Weingarten surface [math], if [math] is the number of times a closed geodesic winds around the axis of rotation and [math] is the number of times the geodesic oscillates about the equator, then [math] when [math] and [math] when [math]. In this paper, we present another proof of Alexander’s result for the Weingarten surfaces [math] that is simpler and more direct. Our approach uses sharp estimates of certain improper integrals to obtain the intervals for permissible ratios [math]. We numerically compute a number of closed geodesics for various combinations of [math] to illustrate the variety of patterns that are possible.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"48 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Closed Geodesics on Weingarten Surfaces with [math]\",\"authors\":\"Frank E. Baginski, Valério Ramos Batista\",\"doi\":\"10.1137/23m1608616\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1705-1719, September 2024. <br/> Abstract.In 2006, Alexander proved a result that implies for a Weingarten surface [math], if [math] is the number of times a closed geodesic winds around the axis of rotation and [math] is the number of times the geodesic oscillates about the equator, then [math] when [math] and [math] when [math]. In this paper, we present another proof of Alexander’s result for the Weingarten surfaces [math] that is simpler and more direct. Our approach uses sharp estimates of certain improper integrals to obtain the intervals for permissible ratios [math]. We numerically compute a number of closed geodesics for various combinations of [math] to illustrate the variety of patterns that are possible.\",\"PeriodicalId\":49534,\"journal\":{\"name\":\"SIAM Journal on Applied Dynamical Systems\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1608616\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1608616","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 应用动力系统期刊》，第 23 卷第 3 期，第 1705-1719 页，2024 年 9 月。摘要.2006 年，亚历山大证明了一个结果，即对于魏格登曲面[math]，如果[math]是闭合大地线绕旋转轴旋转的次数，[math]是大地线绕赤道摆动的次数，则当[math]为[math]时，[math]为[math]；当[math]为[math]时，[math]为[math]。在本文中，我们提出了亚历山大对魏格登曲面[math]结果的另一个证明，它更简单、更直接。我们的方法是利用某些不完全积分的尖锐估计来获得允许比率的区间[math]。我们用数值计算了[math]的各种组合的闭合大地线，以说明可能存在的各种模式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Closed Geodesics on Weingarten Surfaces with [math]

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1705-1719, September 2024.
Abstract.In 2006, Alexander proved a result that implies for a Weingarten surface [math], if [math] is the number of times a closed geodesic winds around the axis of rotation and [math] is the number of times the geodesic oscillates about the equator, then [math] when [math] and [math] when [math]. In this paper, we present another proof of Alexander’s result for the Weingarten surfaces [math] that is simpler and more direct. Our approach uses sharp estimates of certain improper integrals to obtain the intervals for permissible ratios [math]. We numerically compute a number of closed geodesics for various combinations of [math] to illustrate the variety of patterns that are possible.

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

来源期刊

SIAM Journal on Applied Dynamical Systems 物理-物理：数学物理

CiteScore

3.60

自引率

4.80%

发文量

审稿时长

6 months

期刊介绍： SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.