Asymptotic Average Shadowing Property for Flows

Abstract

In this paper we show that if X is a compact metric space and φ : ℝ × X → X is a flow and φ is weak uniformly almost periodic with positively asymptotic average shadowing property, then φ is strongly ergodic. As well as corollary we show that if φ : ℝ × X → X is a Lyapunov stable flow with the asymptotic average shadowing property then φ is not distal.

Keywords:

• Asymptotic average shadowing property δ-average-pseudo-orbit
• Lyapunov stable
• strongly ergodic