Two-dimensional global manifolds of vector fields

We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger p ieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important featu res of dynamical behavior. For illustration, we compute the stable manifold of the origin spiralling into the Lorenz attractor, and an unstable manifo ld in zeta(3)-model converging to an attracting limit cycle. (C) 1999 Ameri can Institute of Physics. [S1054-1500(99)02403-9].