动态系统的收缩阴影特性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-19 DOI:10.1007/s12346-024-01079-9

Noriaki Kawaguchi

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引用次数: 0

摘要

对于由紧凑度量空间的连续自映射定义的拓扑动力系统，我们考虑收缩阴影性质，即立普希兹常数小于 1 的立普希兹阴影性质。我们证明了收缩阴影的一些基本性质，并证明非退化同构不具有收缩阴影性质。然后，我们考虑超对称空间的情况。我们还讨论了在收缩阴影假设下链循环集的谱分解。我们给出了几个例子来说明这些结果。

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Contractive Shadowing Property of Dynamical Systems

For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove some basic properties of contractive shadowing and show that non-degenerate homeomorphisms do not have the contractive shadowing property. Then, we consider the case of ultrametric spaces. We also discuss the spectral decomposition of the chain recurrent set under the assumption of contractive shadowing. Several examples are given to illustrate the results.

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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.