Delay equations and radiation damping

Starting from delay equations that model field retardation effects, we stud y the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardati on effects are small, we argue that the physically significant solutions be long to the so-called slow manifold of the system and we identify this inva riant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not containe d in the local equations of motion. (C) 2001 Elsevier Science B,V. All righ ts reserved.