{"title":"Finsler三维球面上的多个封闭测地线","authors":"Huagui Duan , Zihao Qi","doi":"10.1016/j.jfa.2025.110863","DOIUrl":null,"url":null,"abstract":"<div><div>In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we prove this conjecture for a bumpy Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> if the Morse index of any prime closed geodesic is nonzero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110863"},"PeriodicalIF":1.6000,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiple closed geodesics on Finsler 3-dimensional sphere\",\"authors\":\"Huagui Duan , Zihao Qi\",\"doi\":\"10.1016/j.jfa.2025.110863\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we prove this conjecture for a bumpy Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> if the Morse index of any prime closed geodesic is nonzero.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"288 10\",\"pages\":\"Article 110863\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002212362500045X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/2/10 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002212362500045X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/10 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multiple closed geodesics on Finsler 3-dimensional sphere
In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler . In this paper, we prove this conjecture for a bumpy Finsler if the Morse index of any prime closed geodesic is nonzero.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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