Monday, May 19

4:00 PM-6:00 PM Magpie A & B - Level B

Computing Invariant Manifolds

Geometric desciptions of dynamical systems include varied types of invariant manifolds, including stable and unstable manifolds of equilibrium points and periodic orbits, normally hyperbolic invariant manifolds, manifolds of equilibria in families and bifurcation sets in multiparameter families. This minisymposium will highlight computational methods to determine invariant manifolds of dimension larger than one. The algorithmic basis for such computations is not firmly established and is undergoing rapid evolution. The problems entail significantly greater geometric complexity than is encountered in the computation of invariant curves. The speakers will describe their experiences in implementing calculations of two dimensional invariant manifolds on example problems.

Organizer: John Guckenheimer
Cornell University

4:00 Computing Stable Sets of Noninvertible Mappings
Frederick J. Wicklin and Chia-Hsing Nien, University of Minnesota, Minneapolis
4:30 Computation of Heteroclinic Two-Dimensional Invariant Manifold Interactions
Mark E. Johnson, Princeton University; Michael S. Jolly, Indiana University, Bloomington; Ioannis G. Kevrekidis, Princeton University; and John Lowengrub, University of Minnesota, Minneapolis
5:00 Computing Invariant Manifolds of Saddle-Type
Hinke Osinga, University of Minnesota, Minneapolis
5:30 Stable and Unstable Manifolds of Halo Orbits in the Circular Restricted Three-body Problem
Robert Thurman and Patrick Worfolk, University of Minnesota, Minneapolis

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TMP, 4/3/97
MMD, 5/7/97