NORMAL FORMS FOR RETARDED FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH PARAMETERS AND APPLICATIONS TO HOPF-BIFURCATION

The paper addresses, for retarded functional differential equations (F DEs) with parameters, the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to an inva riant space for the infinitesimal generator of the linearized equation at a singularity. The analysis is based on the theory previously deve loped for FDEs without parameters by considering an extension of a pha se space appropriate to the computation of these normal forms. As an a pplication, the generic Hopf bifurcation for scalar retarded FDEs is c onsidered. (C) 1995 Academic Press, Inc.