连续流的平均阴影性质与混沌

IF 0.4 Q4 MATHEMATICS

Journal of Dynamical Systems and Geometric Theories Pub Date : 2017-07-03 DOI:10.1080/1726037X.2017.1390190

Ying-xuan Niu

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引用次数: 3

摘要

设X为紧度量空间，φ: R × X→X为连续流。在本文中，我们证明了如果φ具有平均阴影性质并且φ的概周期点在X中是密集的，则φ × φ是拓扑遍历的。作为推论，我们得到，如果一个李雅普诺夫稳定流φ具有平均阴影性质，那么X是一个单态。

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The average shadowing property and chaos for continuous flows

Abstract Let X be a compact metric space and ϕ : R × X → X be a continuous flow. In this paper, we prove that if ϕ has the average shadowing property and the almost periodic points of ϕ are dense in X, then ϕ × ϕ is topologically ergodic. As a corollary, we obtain that if a Lyapunov stable flow ϕ has the average-shadowing property, then X is a singleton.

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Journal of Dynamical Systems and Geometric Theories MATHEMATICS-

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