Center manifolds for Random Dynamical Systems with generalized trichotomies

TL;DR

This paper proves the existence of invariant center manifolds for small perturbations of linear random dynamical systems with generalized trichotomies, applicable in both continuous and discrete time, supported by illustrative examples.

Contribution

It introduces the first results on invariant center manifolds for systems with generalized trichotomies under random perturbations.

Findings

Existence of invariant center manifolds in continuous and discrete time.

Applicability to systems with generalized trichotomies.

Illustrative examples demonstrating the theory.

Abstract

For small perturbations of linear Random Dynamical Systems evolving on a Banach space and exhibiting a generalized form of trichotomy, we prove the existence of invariant center manifolds, both in continuous and discrete-time. Furthermore, we provide several illustrative examples.