随机摄动Hopf系统剪切混沌的计算机辅助证明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-01-05 DOI:10.1214/22-aap1841

M. Breden, Maximilian Engel

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引用次数: 7

摘要

我们证实了一个长期存在的关于具有Hopf分岔的随机摄动系统中剪切引起混沌的猜想。显示主要混沌性质的方法，即正李雅普诺夫指数，是一种计算机辅助证明。利用最近发展的有界域上条件Lyapunov指数理论和改进的Furstenberg-Khasminskii公式，问题归结为描述潜在随机过程分布的Kolmogorov算子的特征函数的严格计算。

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Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process.

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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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