CAM colloquium - Friday, February 11
3:30 p.m.
655 Rhodes Hall

Michael E. Henderson
IBM Watson Research Center

"Computing Invariatn Manifolds by Covering Them with Fat Trajectories"

Abstract:

I will describe an algorithm for computing invariant manifolds that are the image of a smooth (k-1) dimensional surface under a flow. The manifold is covered by the image of neighborhoods on the surface under the flow (fat trajectories). For example, when k=1 the neighborhoods are intervals and the fat trajectories are ribbons, when k=2 the neighborhoods are circular disks and the fat trajectories circular tubes.

To implement this algorithm equations must be derived for the fat trajectory, and a way must be found to interpolate points between diverging fat trajecties so
that new fat trajectories can be started. I will discuss both of these issues, describe how to maintain a represention of the manifold as a set of overlapping
spherical charts, and show a computation of the stable manifold of the origin in Lorenz's system.

Refreshments at 4:30 in 657 Rhodes Hall.