Globalizing two-dimensional unstable manifolds of maps (joint work with Bernd Krauskopf)

Hinke Osinga, The Geometry Center, University of Minnesota at Minneapolis

We present an algorithm for computing the global two-dimensional unstable manifold of a normally hyperbolic invariant circle of a three-dimensional map. Our algorithm computes intersections of the unstable manifold with a finite number of leaves of a chosen linear foliation. This allows us to guarantee the quality of the mesh on this manifold. We compute growing pieces of the unstable manifold by using a method that does not depend on the dynamics on the manifold. Our method can also be used for the computation of global two-dimensional unstable manifolds of hyperbolic saddle points. The global stable manifold is obtained by considering the inverse map.