Inertial Manifolds for Random Differential Equations

Abstract

The intention of the article is to show the existence of inertial manifolds for random dynamical systems generated by infinite dimensional random evolution equations. To find these manifolds we formulate a random graph transform. This transform allows us to introduce a random dynamical system on graphs. A random fixed point of this system defines the graph of the inertial manifold. In contrast to other publications dealing with these objects we also suppose that the linear part of such an evolution equation contains random operators. To deal with these objects we apply th e multiplicative ergodic theorem. The key assumption for the existence of an inertial manifold is an ω-wise gap condition.