可逆系统中的非扭曲退化低维不变环的持续性

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-23 DOI:10.1007/s12346-024-01108-7

Xiaomei Yang, Junxiang Xu

{"title":"可逆系统中的非扭曲退化低维不变环的持续性","authors":"Xiaomei Yang, Junxiang Xu","doi":"10.1007/s12346-024-01108-7","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we consider nearly integrable reversible systems, whose unperturbed part has a degenerate equilibrium point and a degenerate frequency mapping. Based on the topological degree theory and some KAM techniques, we prove that the non-twist lower dimensional invariant torus with prescribed frequencies persists under small perturbations.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"43 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Persistence of the Non-twist Degenerate Lower Dimensional Invariant Torus in Reversible Systems\",\"authors\":\"Xiaomei Yang, Junxiang Xu\",\"doi\":\"10.1007/s12346-024-01108-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we consider nearly integrable reversible systems, whose unperturbed part has a degenerate equilibrium point and a degenerate frequency mapping. Based on the topological degree theory and some KAM techniques, we prove that the non-twist lower dimensional invariant torus with prescribed frequencies persists under small perturbations.</p>\",\"PeriodicalId\":48886,\"journal\":{\"name\":\"Qualitative Theory of Dynamical Systems\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Qualitative Theory of Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12346-024-01108-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01108-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑了近可积分可逆系统，其未扰动部分具有退化平衡点和退化频率映射。基于拓扑度理论和一些 KAM 技术，我们证明了具有规定频率的非扭曲低维不变环在小扰动下持续存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Persistence of the Non-twist Degenerate Lower Dimensional Invariant Torus in Reversible Systems

查看原文本刊更多论文

Persistence of the Non-twist Degenerate Lower Dimensional Invariant Torus in Reversible Systems

In this paper, we consider nearly integrable reversible systems, whose unperturbed part has a degenerate equilibrium point and a degenerate frequency mapping. Based on the topological degree theory and some KAM techniques, we prove that the non-twist lower dimensional invariant torus with prescribed frequencies persists under small perturbations.

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

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.