Skip to content

Global manifolds of vector fields : the general case

Research output: Working paperWorking paper and Preprints

  • HM Osinga
  • B Krauskopf
Original languageEnglish
StateUnpublished - 1999


For any 1 <k <n, we show how to compute the k-dimensional stable or unstable manifold of an equilibrium in a vector field with an n-dimensional phase space. The manifold is grown as concentric (topological) (k-1)-spheres, which are computed as a set of intersection points of the manifold with a finite number of hyperplanes perpendicular to the last (k-1)-sphere. These intersection points are found by solving a suitable boundary value problem. In combination with a method for adding or removing hyperplanes we ensure that the mesh that represents the computed manifold is of a prescribed quality. As examples we compute two-dimensional stable manifolds in the Lorenz system and in a four-dimensional Hamiltonian system from optimal control theory. This paper has been revised in September 1999.

Download statistics

No data available




View research connections

Related faculties, schools or groups

  1. Global manifolds of vector fields : The general case

    Research output: Contribution to journalArticle