Shadowing in random dynamical systems

Pages: 355 - 362, Volume 12, Issue 2, February 2005

doi:10.3934/dcds.2005.12.355       Abstract        Full Text (188.4K)       Related Articles

Lianfa He - College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, China (email)
Hongwen Zheng - Institute of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China (email)
Yujun Zhu - College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, China (email)

Abstract: In this paper we consider the shadowing property for $C^1$ random dynamical systems. We first define a type of hyperbolicity on the full measure invariant set which is given by Oseledec's multiplicative ergodic theorem, and then prove that the system has the "Lipschitz" shadowing property on it.

Keywords:  Random dynamical system, multiplicative ergodic theorem, shadowing property.
Mathematics Subject Classification:  37C50, 37H99.

Received: August 2003;      Revised: August 2004;      Published: December 2004.