Algorithms for constructing stable manifolds of stationary solutions

Algorithms for computing stable manifolds of hyperbolic stationary solutions of autonomous systems are of two types: either the aim is to compute a single point on the manifold or the entire (local) manifold. Traditionally only indirect methods have been considered, i.e. first the continuous problem is discretized by a one-step scheme and then the Liapunov-Perron or Hadamard graph transform are applied to the resulting discrete dynamical system. We will consider different variants of these indirect methods but also algorithms of the above two types which are applied directly to the continuous problem.