First-time Sensitive Homeomorphisms

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-09 DOI:10.1007/s10884-024-10362-x

Mayara Antunes, Bernardo Carvalho

引用次数: 0

Abstract

We introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expansive homeomorphisms, the shift map on the Hilbert cube, and also some partially hyperbolic diffeomorphisms satisfy this condition. We prove the existence of local unstable continua satisfying similar properties with the local unstable continua of continuum-wise expansive homeomorphisms, but assuming first-time sensitivity. As a consequence we prove that first-time sensitivity (with some additional technical assumptions) implies positive topological entropy.

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首次敏感同构

我们介绍了紧凑度量空间同构的首次敏感性，即空间开球的首次增大次数的条件。连续膨胀同构、希尔伯特立方体上的移动映射以及一些部分双曲差同构都满足这个条件。我们证明了局部不稳定连续面的存在，其性质与连续膨胀同态的局部不稳定连续面相似，但假定了首次敏感性。因此，我们证明了首次敏感性（加上一些额外的技术假设）意味着正拓扑熵。

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.