# American Institute of Mathematical Sciences

February  2005, 12(2): 355-362. doi: 10.3934/dcds.2005.12.355

## Shadowing in random dynamical systems

 1 College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, China, China 2 Institute of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

Received  August 2003 Revised  August 2004 Published  December 2004

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.
Citation: Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355
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