Invariant Manifolds for Functional Differential Equations Close to Ordinary Differential Equations

This paper considers invariant manifolds of global trajectories of retarded Functional Differential Equations in Rn. The persistence, smoothness and stability of such manifolds where the flow is given by an Ordinary Differential Equation (ODE) in Rn is studied for small perturbations of ODEs. The novelty of the present approach lies in the use of the dynamics of the flow on the manifolds, instead of their attractivity properties