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Optimal estimates along stable manifolds of non-uniformly hyperbolic dynamics

Published online by Cambridge University Press:  28 July 2008

Luis Barreira  and
Claudia Valls
Luis Barreira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
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Abstract

We establish the persistence of the asymptotic stability of a linear equation $v'=A(t)v$ in a Banach space under sufficiently small perturbations, when the linear equation admits a non-uniform exponential contraction or a non-uniform exponential dichotomy. Moreover, we obtain optimal estimates for the decay of solutions of the perturbed equation, that in general may depend on the initial time.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 4 , August 2008 , pp. 693 - 717
Copyright
2008 Royal Society of Edinburgh

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