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Structural stability of linear random dynamical systems

Published online by Cambridge University Press:  14 October 2010

Nguyen Dinh Cong
Nguyen Dinh Cong
Affiliation:
Institut für Dynamische Systeme, Universität Bremen, Postfach 330 440, 28334 Bremen, Germany
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Abstract

In this paper, structural stability of discrete-time linear random dynamical systems is studied. A random dynamical system is called structurally stable with respect to a random norm if it is topologically conjugate to any random dynamical system which is sufficiently close to it in this norm. We prove that a discrete-time linear random dynamical system is structurally stable with respect to its Lyapunov norms if and only if it is hyperbolic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1207 - 1220
Copyright
Copyright © Cambridge University Press 1996

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