Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform e...

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Bibliographic Details
Published in:arXiv.org 2013-12
Main Authors: Bento, António J G, Silva, César M
Format: Article
Language:English
Subjects:
Banach spaces
Dichotomies
Differential equations
Liapunov exponents
Manifolds
Operators (mathematics)
Polynomials
Online Access:Get full text
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Summary:We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.
ISSN:2331-8422
DOI:10.48550/arxiv.1007.5039