Hyers–Ulam stability for hyperbolic random dynamics
Volume 255 / 2021
Fundamenta Mathematicae 255 (2021), 69-90
MSC: Primary 37C50, 34D09; Secondary 34D10.
DOI: 10.4064/fm971-10-2020
Published online: 1 April 2021
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, 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.
