B. KRAUSKOPF
Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK
H. M. OSINGA
Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK
E. J. DOEDEL
Department of Computer Science, Concordia University, 1455 Boulevard de Maisonneuve O., Montréal Québec, H3G 1M8, Canada
M. E. HENDERSON
IBM Research, PO Box 218, Yorktown Heights, NY 10598, USA
J. GUCKENHEIMER
Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853–4201, USA
A. VLADIMIRSKY
Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853–4201, USA
M. DELLNITZ
Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany
O. JUNGE
Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany

Received May 14, 2004
Revised June 16, 2004

The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example — the two-dimensional stable manifold of the origin in the Lorenz system.

Stable and unstable manifolds; numerical methods; Lorenz equations