Bernd Krauskopf Theoretical Physics Free University De Boelelaan 1081 1081 HV Amsterdam The Netherlands berndk@nat.vu.nl 
Hinke Osinga The Geometry Center University of Minnesota 1300 South Second Street Minneapolis, MN 55454 U.S.A hinke@geom.umn.edu 
The map in question may be defined explicitly or as the Poincaré map
of a vector field. The latter allows us to compute the
twodimensional unstable manifold that corresponds to a
threedimensional manifold of a normally hyperbolic torus or a limit
cycle in dimension four. The performance of our algorithm is
demonstrated with examples of the different cases. The choices for the
foliation are discussed.
To appear in Int. J. Bifurcation & Chaos

1. Introduction 2. Overview of earlier methods 3. The algorithm 

3.1 Iterating a fundamental domain 3.2 Globalization by adding discrete circles 3.3 The case of a hyperbolic fixed point 3.4 Mesh adaptation 

4. Correctness 5. Examples 

5.1 The 3Dfattened 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 HopfHopf bifurcation 

6. Discussion Acknowledgments References Figures Animations 
Written by: Bernd Krauskopf
& Hinke Osinga
Comments to:
hinke@geom.umn.edu
Created: May 8 1997 
Last modified: Thu Sep 11 17:02:35 1997