On dissipative systems perturbed by bounded random kick-forces

Sergei Kuksin; Armen Shirikyan

doi:10.1017/S0143385702000986

On dissipative systems perturbed by bounded random kick-forces

Sergei Kuksin, Armen Shirikyan

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 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 µ, which is unique among all measures supported by A. Here we show that µ is the unique stationary measure for the RDS in the whole space and study its ergodic properties.

Original language	English
Pages (from-to)	1487-1495
Number of pages	9
Journal	Ergodic Theory and Dynamical Systems
Volume	22
Issue number	5
DOIs	https://doi.org/10.1017/S0143385702000986
Publication status	Published - Oct 2002

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AB - 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 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 µ, which is unique among all measures supported by A. Here we show that µ is the unique stationary measure for the RDS in the whole space and study its ergodic properties.

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On dissipative systems perturbed by bounded random kick-forces

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