Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-28 DOI:10.1007/s10884-023-10342-7

Daniel Gonçalves, Bruno B. Uggioni

引用次数: 0

Abstract

In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism (the Deaconu–Renault system) associated with a directed graph, we completely characterize the shadowing property in terms of conditions on sets of paths. Using these results, we single out classes of graphs for which the associated system presents the shadowing property, fully characterize the shadowing property for systems associated with certain graphs, and show that the system associated with the rose of infinite petals presents the shadowing property and that the Renewal shift system does not present the shadowing property.

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局部同构的阴影，及其在无限图边缘移动空间中的应用

在本文中，我们发展了度量局部紧凑空间局部同构的阴影属性的基本理论，重点是与 C* 代数理论相关的边移空间的应用。对于与有向图相关的局部同构（Deaconu-Renault 系统），我们用路径集的条件完全描述了阴影性质。利用这些结果，我们选出了相关系统呈现阴影性质的图类，完全描述了与某些图相关的系统的阴影性质，并证明了与无限花瓣玫瑰相关的系统呈现阴影性质，而 Renewal shift 系统不呈现阴影性质。

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.