Question

(From SIAM web site.) The behavior of a dynamical system is determined by its "skeleton," which consists of the different attractors (steady states, periodic solutions, or more complicated sets), as well as saddle-type objects with their global stable and unstable manifolds. Global manifolds are complicated objects that must be found numerically. They are hypersurfaces consisting of infinitely many trajectories that end up (or come from) a saddle-type object. All other trajectories qualitatively follow the dynamics given by the "nearest" global manifolds. This feature was recently utilized in the Genesis Mission, which sent a spacecraft to a saddle-type periodic orbit around the Lagrange point between the earth and the sun to collect solar dust particles. The spacecraft traveled on global manifolds to its destination and back to earth virtually without any fuel.