Nonuniform dichotomic behavior: Lipschitz invariant manifolds for ODEs

Abstract

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new situations that are far from the hyperbolic setting, our results include, and sometimes improve, some known stable manifold theorems.

Final version with minor changes. Accepted for publication in Bulletin des Sciences Mathématiques. arXiv admin note: text overlap with arXiv:1209.6589