向量场奇异点的李亚普诺夫稳定性问题中的集合论病理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-02 DOI:10.1007/s11784-024-01111-0

Yu. Ilyashenko

引用次数: 0

摘要

我们证明了李亚普诺夫稳定性问题甚至在集合论层面上也表现出了病态。也就是说，存在一个向量场 5 射流的解析单参数族，它通过一个不相交区间的可数联合与稳定射流集交叉。

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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Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields

We prove that Lyapunov stability problem demonstrates pathologies even on the set-theoretical level. Namely, there exists an analytic one-parameter family of 5-jets of vector fields that crosses the set of stable jets by a countable union of disjoint intervals.

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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.