A New Algorithm for the Numerical Approximation of an Invariant Curve

Abstract

This paper describes a new algorithm for the numerical approximation of an invariant curve for a system of ordinary differential equations. The algorithm is based on the stability properties of the invariant curve. It is possible to approximate stable invariant curves with vanishing rotation number by means of the new algorithm. Numerical examples, for the driven van der Pol equation and the delay logistic equation, illustrate the possibilities of the proposed algorithm.