强单调动力系统中可观测混沌的不存在性及其鲁棒性

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2022-03-06 DOI:10.1142/s0219493722400408

Yi Wang, Jinxiang Yao

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引用次数: 0

摘要

对于Banach空间上的强单调动力系统，我们证明了在测度论意义上，最大Lyapunov指数λ max >在一个shy集合上成立。这表明强单调动力系统不承认可观察到的混沌，混沌的概念是由L.S. Young提出的。进一步证明了系统在c1 -扰动下无可见混沌现象的鲁棒性。

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Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems

For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent λ max > 0 holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the C 1 -perturbation of the systems.

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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.