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Invariant Manifolds for Random Dynamical Systems on Banach Spaces Exhibiting Generalized Dichotomies

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Abstract

We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the asymptotic behavior in the invariant manifold is similar to the one of the linear Random Dynamical System.

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Acknowledgements

This work was partially supported by Fundação para a Ciência e Tecnologia through Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI), project UIDB/MAT/00212/2020.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade da Beira Interior, 6201-001, Covilhã, Portugal

    António J. G. Bento & Helder Vilarinho

  2. Centro de Matemática e Aplicações, Universidade da Beira Interior, 6201-001, Covilhã, Portugal

    António J. G. Bento & Helder Vilarinho

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  1. António J. G. Bento
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  2. Helder Vilarinho
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Correspondence to António J. G. Bento.

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Bento, A.J.G., Vilarinho, H. Invariant Manifolds for Random Dynamical Systems on Banach Spaces Exhibiting Generalized Dichotomies. J Dyn Diff Equat 33, 111–133 (2021). https://doi.org/10.1007/s10884-020-09888-7

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  • DOI: https://doi.org/10.1007/s10884-020-09888-7

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