Globalizing Two-Dimensional Unstable Manifolds of Maps

Abstract

We present an algorithm for computing the global two-dimensional unstable manifold of a hyperbolic fixed point or a normally hyperbolic invariant circle of a three-dimensional map. The global stable manifold can be obtained by considering the inverse map. Our algorithm computes intersections of the unstable manifold with a finite number of leaves of a chosen linear foliation. In this way, we obtain a growing piece of the unstable manifold represented by a mesh of prescribed quality. The performance of the algorithm is demonstrated with several examples.