Geometric methods for computing invariant manifolds
The purpose of this paper is to contrast the different algorithms obtained for various invariant manifolds when different parametrisations are used. After choosing an appropriate parametrisation for a given type of invariant manifolds, a system of equations is constructed which the representation with respect to this parametrisation must satisfy. Hence, different methods are obtained for computing the invariant manifolds. The author considers one-dimensional manifolds (periodic orbits, connecting orbits between stationary solutions, and stable manifolds of fixed points), and two-dimensional ones (invariant tori for autonomous systems, invariant curves for periodically forced systems, and stable manifolds of fixed points).
scientific article; zbMATH DE number 803530
scientific article