STOCHASTIC VERSIONS OF HARTMAN–GROBMAN THEOREMS

Abstract

We present versions of Hartman–Grobman theorems for random dynamical systems (RDS) in the discrete case. We use the same random norm like in Wanner [14], but instead of using difference equations, we perform an appropriate generalization of the deterministic arguments in an adequate space of measurable homeomorphisms to extend the results in [14] with weaker hypotheses (integrability instead of boundedness) and simpler arguments.