Open Access
Article
The average shadowing property and chaos for continuous flows
*Yingxuan NiuCorresponding authoryxniu@wxc.edu.cnDepartment of MathematicsWest Anhui UniversityLu’an, Anhui, 237012, ChinaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 Mar 2017
- Accepted:
- 29 Jun 2017
- Published Online:
- 06 Dec 2017
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2017.1390190
- Pages:
- 99–109
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.
Keywords
Subject Classifications
54H2037D3037C50
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