An efficient method for computing invariant manifolds of planar maps

Abstract An efficient method for computing invariant manifolds of mappings in the plane is described and compared to a simple method in common use. The emphasis is on numerically producing smoothly resolved segments of invariant manifolds of arbitrary length while requiring a minimum number of calls to the map itself. A brief estimate of errors is given and applications are discussed. Qualitative and quantitative comparisons between the two methods are made using an example problem. The present method is applied to computing unstable manifolds for the well-know periodically forced Duffing system and the Henon map (for which the manifold is a strange attractor).