Generalized nonuniform dichotomies and local stable manifolds

Details Generalized nonuniform dichotomies and local stable manifolds Generalized nonuniform dichotomies and local stable manifolds

2010-07-28

arxiv.org/abs/1007.5039v1

Mathematics

Dynamical Systems

17 pages

Scientific paper

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.

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