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
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .