Manchester Applied Mathematics and Numerical Analysis Seminars

Winter 2000/2001

October 25, 2000, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Two-dimensional global manifolds of vector fields

Dr. Hinke Osinga, School of Mathematical Sciences, University of Exeter
(joint work with Bernd Krauskopf, University of Bristol)

We present an algorithm for computing two-dimensional stable and unstable manifolds of 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.

This method works well for the computation of two-dimensional manifolds of three-dimensional vector fields, but can also be used for higher dimensional cases. In particular, we give an example of a two-dimensional manifold for a four-dimensional system. We also discuss manifolds of periodic orbits that may be non-orientable.

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For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).

Page last modified: 18 September, 2000

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