Shadowing in random dynamical systems

Lianfa He; Hongwen Zheng; Yujun Zhu

doi:10.3934/dcds.2005.12.355

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2005, Volume 12, Issue 2: 355-362. Doi: 10.3934/dcds.2005.12.355

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Shadowing in random dynamical systems

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

Received: August 2003

Revised: August 2004

Published: February 2005

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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.

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Mathematics Subject Classification: 37C50, 37H99.

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