On perturbations of delay-differential equations with periodic orbits

Equations of retarded type and simple neutral-type equations are considered. The study concerns both autonomous and non-autonomous perturbations of an autonomous equation which possesses a non-trivial periodic orbit. The main tool is a local coordinate system around the periodic orbit which is obtained from the phase space decomposition via Floquet multipliers. Under the assumption that the perturbation function is Lipschitz the existence of an integral manifold with periodic structure for the system in the new coordinates is shown. This implies that, under autonomous perturbations, periodic orbits are continued. Furthermore, we give a description of the flow on the center manifold of the periodic orbit.