AN ALGORITHMIC SCHEME FOR APPROXIMATING CENTER MANIFOLDS AND NORMAL FORMS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract

Normal forms theory is one of the most powerful tools in the study of nonlinear dynamical systems, in particular, for stability and bifurcation analysis. In the context of finite-dimensional ordinary differential equations (ODEs), this theory can be traced back to the work done a hundred years ago by Poincaré [14]. The basic idea of normal form consists of employing successive, near-identity, nonlinear transformations, which leads us to a differential equation in a simpler form, qualitatively equivalent to the original system in the vicinity of a fixed equilibrium point, thus hopefully greatly simplifying the dynamical analysis.