ALGORITHMS FOR COMPUTING NORMALLY HYPERBOLIC INVARIANT-MANIFOLDS

An efficient algorithm is developed for the numerical computation of n ormally hyperbolic invariant manifolds, based on the graph transform a nd Newton's method. It fits in the perturbation theory of discrete dyn amical systems and therefore allows application to the setting of cont inuation. A convergence proof is included. The scope of application is not restricted to hyperbolic attractors, but extends to normally hype rbolic manifolds of saddle type. It also computes stable and unstable manifolds. The method is robust and needs only little specification of the dynamics, which makes it applicable to e.g. Poincare maps. Its pe rformance is illustrated on examples in 2D and 3D, where a numerical d iscussion is included.