{"title":"具有退化频率映射的可逆系统中多尺度退化不变环的持续性","authors":"Xiaomei Yang, Junxiang Xu","doi":"10.1134/S1560354724040051","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers a class of nearly integrable reversible systems\nwhose unperturbed part has a degenerate frequency mapping and a degenerate equilibrium point.\nBased on some KAM techniques\nand the topological degree theory, we prove the persistence of multiscale degenerate hyperbolic lower-dimensional invariant tori with prescribed frequencies.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"605 - 619"},"PeriodicalIF":0.8000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping\",\"authors\":\"Xiaomei Yang, Junxiang Xu\",\"doi\":\"10.1134/S1560354724040051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers a class of nearly integrable reversible systems\\nwhose unperturbed part has a degenerate frequency mapping and a degenerate equilibrium point.\\nBased on some KAM techniques\\nand the topological degree theory, we prove the persistence of multiscale degenerate hyperbolic lower-dimensional invariant tori with prescribed frequencies.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"29 and Dmitry Treschev)\",\"pages\":\"605 - 619\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354724040051\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724040051","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping
This paper considers a class of nearly integrable reversible systems
whose unperturbed part has a degenerate frequency mapping and a degenerate equilibrium point.
Based on some KAM techniques
and the topological degree theory, we prove the persistence of multiscale degenerate hyperbolic lower-dimensional invariant tori with prescribed frequencies.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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