Optimal estimates along stable manifolds of non-uniformly hyperbolic dynamics
Published online by Cambridge University Press: 28 July 2008
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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