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

Written by: Bernd Krauskopf
& Hinke Osinga

Created: May 27 1997 ---
Last modified: Fri May 30 19:53:24 1997