Shadowing in random dynamical systems

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

Shadowing in random dynamical systems

Lianfa He ^1, , Hongwen Zheng ^2, and Yujun Zhu ^1,

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

Abstract
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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: multiplicative ergodic theorem, shadowing property., Random dynamical system.

Mathematics Subject Classification: 37C50, 37H9.

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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