Decay of correlations for some non-uniformly hyperbolic attractors

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023128

Sebastian Burgos

引用次数: 0

Abstract

We study the decay of correlations for certain dynamical systems with non-uniformly hyperbolic attractors, which natural invariant measure is the Sinai-Ruelle-Bowen (SRB) measure. The system $ g $ that we consider is produced by applying the slow-down procedure to a uniformly hyperbolic diffeomorphism $ f $ with an attractor. Under certain assumptions on the map $ f $ and the slow-down neighborhood, we show that the map $ g $ admits polynomial upper and lower bounds on correlations with respect to its SRB measure and the class of Hölder continuous observables. Our results apply to the Smale-Williams solenoid, as well as its sufficiently small perturbations.

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一些非一致双曲吸引子的相关衰减

研究了一类具有非一致双曲吸引子的动力系统的相关性衰减，该系统的自然不变测度为Sinai-Ruelle-Bowen (SRB)测度。将慢化过程应用于具有吸引子的一致双曲微分同胚$ f $，得到了我们所考虑的系统$ g $。在映射$ f $和slow-down邻域的某些假设下，我们证明了映射$ g $与其SRB测度和Hölder连续可观测值类的相关性具有多项式上界和下界。我们的结果适用于small - williams螺线管，以及它的足够小的扰动。

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.