Bernd Krauskopf and Hinke Osinga
We present an algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. The main idea is to grow the manifold in concentric (topological) circles. Each new circle is computed as a set of intersection points of the manifold with a finite number of planes perpendicular to the last circle. Together with a scheme for adding or removing such planes this guarantees the quality of the mesh representing the computed manifold.
As examples we compute the stable manifold of the origin spiralling into the Lorenz atractor, and an unstable manifold in Arneodo's system converging to a limit cycle.
|GZIP copy of the ps paper (668KB)|
|Animations of manifolds in the Lorenz system|
|Animations of manifolds in Arneodo's system|