Center Manifolds for Delay Equations

Abstract

We give a streamlined detailed proof of the existence of smooth center invariant manifolds for nonautonomous delay equations for which the linear part has an exponential trichotomy. More precisely, we consider C^k perturbations with Lipschitz kth derivative and we obtain the same regularity for the center manifolds. We first construct Lipschitz center invariant manifolds for nonautonomous delay equations under sufficiently small Lipschitz perturbations.