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Two-dimensional global manifolds of vector fields

Krauskopf, Bernd and Osinga, Hinke (1999) Two-dimensional global manifolds of vector fields. Chaos, 9 (3). pp. 768-774. ISSN 1054-1500. doi:10.1063/1.166450.

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We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger pieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important features of dynamical behavior. For illustration, we compute the stable manifold of the origin spiralling into the Lorenz attractor, and an unstable manifold in zeta(3)-model converging to an attracting limit cycle.

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Additional Information:Copyright © 1999 American Institute of Physics. Received 16 November 1998; accepted 18 May 1999. This work was initiated during the authors’ participation in the Special Year on Emerging Applications of Dynamical Systems 1997/98 at the Institute for Mathematics and its Applications, Minneapolis. We thank W.-J. Beyn, M. Dellnitz, E. J. Doedel, J. Guckenheimer, and M. E. Johnson for helpful discussions, and the IMA for its hospitality and support. B.K. thanks the California Institute of Technology and H.O. the University of Bristol for its hospitality. H. O. was supported by AFOSR/DDRE MURI AFS-5X-F496209610471. Additionally, material can be found in the EPAPS.(22)
Subject Keywords:topology; classical field theory; limit cycles
Issue or Number:3
Record Number:CaltechAUTHORS:KRAchaos99
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1932
Deposited By: Tony Diaz
Deposited On:23 Feb 2006
Last Modified:08 Nov 2021 19:43

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