Computing Invariant Manifolds by Integrating Fat Trajectories

We present a new method of computing a well distributed set of points on k-dimensional manifolds which are invariant under a flow. The method uses on chains of local approximations along trajectories (fat trajectories) to cover the manifold with well spaced points. Points between two diverging fat trajectories are interpolated by either interpolating over a certain dual simplex, or by solving a two point boundary value problem.

We derive formulae for the evolution of a second local approximation of the invariant manifold along a trajectory, show that interpolation points in the cleft where k (the dimension of the manifold) trajectories diverge will exist, and apply the method to the stable manifold of the origin in the "standard" Lorenz system.

By: Michael E. Henderson

Published in: RC22944 in 2003


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