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On dissipative systems perturbed by bounded random kick-forces

Published online by Cambridge University Press:  30 September 2002

SERGEI KUKSIN  and
ARMEN SHIRIKYAN
SERGEI KUKSIN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK and Steklov Institute of Mathematics, 8 Gubkina Street, 117966 Moscow, Russia (e-mail: [email protected])
ARMEN SHIRIKYAN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK and Institute of Mechanics of MSU, 1 Michurinskii Avenue, 119899 Moscow, Russia (e-mail: [email protected])
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Abstract

In this paper, we continue our investigation of dissipative PDE's forced by random bounded kick-forces and of the corresponding random dynamical system (RDS) in function spaces. It has been proved that the domain \mathcal{A} of attainability from zero (which is a compact subset of a function space) is invariant for the RDS associated with the original equation and carries a stationary measure \mu, which is unique among all measures supported by \mathcal{A}. Here we show that \mu is the unique stationary measure for the RDS in the whole space and study its ergodic properties.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 5 , October 2002 , pp. 1487 - 1495
Copyright
© 2002 Cambridge University Press

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