Hyers-Ulam stability for hyperbolic random dynamics

Abstract

We prove that small nonlinear perturbations of random linear dynamics admitting a tempered exponential dichotomy have a random version of the shadowing property. As a consequence, if the exponential dichotomy is uniform, we get that the random linear dynamics is Hyers-Ulam stable. Moreover, we apply our results to study the conservation of Lyapunov exponents of the random linear dynamics subjected to nonlinear perturbations.

Revised version. To appear in Fundamenta Mathematicae

Cited by in corpus (2)

• A general approach to nonautonomous shadowing for nonlinear dynamics
• On the linearization of infinite-dimensional random dynamical systems