Roughness of tempered exponential dichotomies for infinite-dimensional random difference equations

In this paper we study the roughness of tempered exponential dichotomies for linear random dynamical systems in Banach spaces. Such a dichotomy has a tempered bound and describes nonuniform hyperbolicity. We prove the roughness without assuming their invertibility and the integrability condition of...

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Bibliographic Details
Published in:Journal of Differential Equations 2013-05, Vol.254 (9), p.4024-4046
Main Authors: Zhou, Linfeng, Lu, Kening, Zhang, Weinian
Format: Article
Language:English
Subjects:
Cocycle
Random dynamical system
Roughness
Tempered exponential dichotomy
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Summary:In this paper we study the roughness of tempered exponential dichotomies for linear random dynamical systems in Banach spaces. Such a dichotomy has a tempered bound and describes nonuniform hyperbolicity. We prove the roughness without assuming their invertibility and the integrability condition of the Multiplicative Ergodic Theorem. We give an explicit bound for the linear perturbation such that the dichotomy is persistent. We also obtain explicit forms for the exponent and the bound of tempered exponential dichotomy of the perturbed random system in terms of the original ones and the perturbations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2013.02.007