论一维$C^1$$双曲向量场之芽的线性化失败

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2023-12-05 DOI:10.1007/s10884-023-10330-x

Hélène Eynard-Bontemps, Andrés Navas

{"title":"论一维$C^1$$双曲向量场之芽的线性化失败","authors":"Hélène Eynard-Bontemps, Andrés Navas","doi":"10.1007/s10884-023-10330-x","DOIUrl":null,"url":null,"abstract":"We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, \$C^1\$ and \$C^{1+ac}\$ settings.\n","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Failure of Linearization for Germs of $$C^1$$ Hyperbolic Vector Fields in Dimension One\",\"authors\":\"Hélène Eynard-Bontemps, Andrés Navas\",\"doi\":\"10.1007/s10884-023-10330-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, \\\$C^1\\\$ and \\\$C^{1+ac}\\\$ settings.\\n\",\"PeriodicalId\":15624,\"journal\":{\"name\":\"Journal of Dynamics and Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10884-023-10330-x\",\"RegionNum\":4,\"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":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-023-10330-x","RegionNum":4,"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

我们研究了低正则性原点处双曲一维向量场的共轭类。我们通过提供明确的具有相同乘数的互不共轭流的不可数族，证明斯特恩伯格的经典线性化定理在这种情况下严重失效，其中共轭性是在双利普西茨、（C^{1\）和（C^{1+ac}\）情况下考虑的。

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

On the Failure of Linearization for Germs of $$C^1$$ Hyperbolic Vector Fields in Dimension One

We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, $C^1$ and $C^{1+ac}$ settings.

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

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.