Shadowing of the induced map for contracting homeomorphisms

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-10-21 DOI:10.1016/j.jmaa.2024.128983

W. Jung , M. Lee , C.A. Morales

引用次数: 0

Abstract

Let

f : X \to X

be a contracting homeomorphism of a metric space with positive diameter. We prove that the induced map

f_{⁎}

in the space of probability measures equipped with the Prokhorov metric does not have the shadowing property. However, if X is Polish, then the restriction of

f_{⁎}

to the Wasserstein space has the generalized shadowing property as per Boyarsky and Gora [4], concerning the Kantorovich-Rubinstein and Prokhorov metrics.

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收缩同构的诱导映射阴影

设 f:X→X 是具有正直径的度量空间的收缩同构。我们证明，在配有普罗霍罗夫度量的概率度量空间中，诱导映射 f⁎ 不具有阴影性质。然而，如果 X 是波兰的，那么 f⁎ 对 Wasserstein 空间的限制就具有广义阴影性质，正如 Boyarsky 和 Gora [4] 所说的那样，是关于 Kantorovich-Rubinstein 和 Prokhorov 度量的。

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.

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