A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS-Reference-Cited by-同舟云学术

A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS

Published:2005-03 Issue:03 Volume:15 Page:763-791
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

KRAUSKOPF B.¹,OSINGA H. M.¹,DOEDEL E. J.²,HENDERSON M. E.³,GUCKENHEIMER J.⁴,VLADIMIRSKY A.⁴,DELLNITZ M.⁵,JUNGE O.⁵

Affiliation:

1. Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, UK

2. Department of Computer Science, Concordia University, 1455 Boulevard de Maisonneuve O., Montréal Québec, H3G 1M8, Canada

3. IBM Research, PO Box 218, Yorktown Heights, NY 10598, USA

4. Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY 14853–4201, USA

5. Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany

Abstract

The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example — the two-dimensional stable manifold of the origin in the Lorenz system.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127405012533

Reference55 articles.

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