Flow Box Tiling Methods for Compact Invariant Manifolds

Copyright © [2011] by The Society for Industrial and Applied Mathematics. All rights reserved

Invariant manifolds are important to the study of the qualitative behavior of dynamical systems and nonlinear control. Good algorithms exist for finding many one dimensional invariant curves, such as periodic orbits, orbits connecting fixed points, and more recently two dimensional stable and unstable manifolds of fixed points. This paper addresses the problem of computing higher dimensional closed invariant manifolds, for example invariant tori, using an approach that produces a large system of coupled two point boundary value problems.

algorithm described here is not limited to a particular dimension or topology. It does not assume that a closed global section exists, nor that a splitting or parameterization of the manifold is known á priori. A flow box tiling is used to construct a set of trajectory fragments on the manifold which are used to pose a system of coupled two point boundary value problems for the manifold.

By: Michael E. Henderson

Published in: SIAM Journal on Applied Dyamical Systems, volume 20, (no 3), pages 1154-76 in 2011


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