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.
Additional information: Preprint submitted to the International Journal of Bifurcation and Chaos
Sponsorship: The authors thank Mike Jolly for providing the image in Fig. 3 of the Lorenz manifold computed with the method in [Johnson et al., 1997] and seen from the common viewpoint.
- unstable manifolds, Lorenz equation, stable manifolds, numerical methods