Abstract and Contents

5. Examples

Our algorithm does not depend on the dynamics on the circle, and it is not influenced by the ratio of the eigenvalues of the linear part at the hyperbolic fixed point. This is demonstrated in Section 5.1 with the example of the 3D-fattened Arnol'd family. In Section 5.2 we compute stable and unstable manifolds in a family of quasiperiodically forced Henon maps. This shows that the manifolds are allowed to fold as long as the Foliation Condition is satisfied. The regularity of the mesh is illustrated in Section 5.3. Here, we also study the accuracy of our computations. The limitations concerning the Foliation Condition are discussed in Section 5.4, where we compute the stable manifold of the origin in the Lorenz system. Finally, the performance of our algorithm for a Poincare map is demonstrated with the unfolding of the Hopf-Hopf bifurcation in Section 5.5. All figures have been rendered with the package Geomview [Phillips et al. 1993].

5.1 The 3D-fattened Arnol'd family
5.2 Quasiperiodically forced Hénon map
5.3 A saddle surface
5.4 The Lorenz system
5.5 Normal form of the Hopf-Hopf bifurcation

Abstract and Contents

Written by: Bernd Krauskopf & Hinke Osinga
Created: May 27 1997 --- Last modified: Fri May 30 19:53:24 1997