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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-05 DOI:10.1007/s10884-023-10330-x

Hélène Eynard-Bontemps, Andrés Navas

引用次数: 0

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.

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论一维$C^1$$双曲向量场之芽的线性化失败

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。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.