Journal of Dynamics and Differential Equations

, Volume 25, Issue 4, pp 1139–1158

Generalized Nonuniform Dichotomies and Local Stable Manifolds

Article

DOI: 10.1007/s10884-013-9331-4

Cite this article as:
Bento, A.J.G. & Silva, C.M. J Dyn Diff Equat (2013) 25: 1139. doi:10.1007/s10884-013-9331-4

Abstract

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.

Keywords

Invariant manifoldsNonautonomous differential equationsNonuniform generalized dichotomies

Mathematics Subject Classification (2000)

37D1034D0937D25

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal