The Computation of Invariant Sets via Newton’s Method

Abstract

In this paper we present a novel approach to the computation of invariant sets of dynamical systems. Employing a Banach space formalism to describe subsets of Rn, we are able to formulate the property of a set to be invariant as a zero-finding problem. For technical reasons, we restrict ourselves to compact convex sets and use Newton’s method to approximate such invariant sets. The theoretical foundations for realizing this approach are analyzed, and it is illustrated by analytical and numerical examples.