随机摄动Hopf系统剪切混沌的计算机辅助证明

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability 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

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.