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Hyers–Ulam stability for hyperbolic random dynamics

Volume 255 / 2021

Lucas Backes, Davor Dragičević 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.

Authors

  • Lucas BackesDepartamento de Matemática
    Universidade Federal do Rio Grande do Sul
    Av. Bento Gonçalves 9500, CEP 91509-900
    Porto Alegre, RS, Brazil
    e-mail
  • Davor DragičevićDepartment of Mathematics
    University of Rijeka
    Rijeka, Croatia
    e-mail

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