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Pseudo-orbit tracing property for random diffeomorphisms*

Published online by Cambridge University Press:  14 November 2011

Liu Peidong ,
Qian Minping  and
Tang Fuchang
Liu Peidong
Affiliation:
Department of Mathematics, Peking University, Beijing, 100871, P.R. China
Qian Minping
Affiliation:
Department of Probability and Statistics, Peking University, Beijing, 100871, P.R. China
Tang Fuchang
Affiliation:
Department of Probability and Statistics, Peking University, Beijing, 100871, P.R. China
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Abstract

In this paper we consider the pseudo-orbit tracing property for dynamical systems generated by iterations of random diffeomorphisms. We first define a type of hyperbolicity by means of a ‘random’ multiplicative ergodic theorem, and then prove our shadowing result by employing the graph transformation methods. That result applies to, for example, the case of small random diffeomorphisms type perturbations of hyperbolic sets of deterministic dynamical systems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1027 - 1033
Copyright
Copyright © Royal Society of Edinburgh 1996

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