Hyers–Ulam stability for hyperbolic random dynamics
Copyright policy )Hyers–Ulam stability for hyperbolic random dynamics
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
- University of Rijeka Croatia
- Federal University Foundation of Rio Grande Brazil
random dynamical systems, hyperbolicity, Perturbation theory of linear operators, FOS: Mathematics, Hyers-Ulam stability, Spectral operators, decomposable operators, well-bounded operators, etc., Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Stability theory for random and stochastic dynamical systems, Hyers-Ulam stability, hyperbolicity, random dynamical systems
random dynamical systems, hyperbolicity, Perturbation theory of linear operators, FOS: Mathematics, Hyers-Ulam stability, Spectral operators, decomposable operators, well-bounded operators, etc., Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Stability theory for random and stochastic dynamical systems, Hyers-Ulam stability, hyperbolicity, random dynamical systems
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