A survey of methods for computing (un)stable manifolds of vector fields

B Krauskopf; HM Osinga; EJ Doedel; ME Henderson; J Guckenheimer; A Vladimirsky; M Dellnitz; O Junge

A survey of methods for computing (un)stable manifolds of vector fields

B Krauskopf, HM Osinga, EJ Doedel, ME Henderson, J Guckenheimer, A Vladimirsky, M Dellnitz, O Junge

Department of Engineering Mathematics

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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.

Original language	English
Publication status	Unpublished - 2004

Bibliographical note

Additional information: Preprint submitted to the International Journal of Bifurcation and Chaos

Sponsorship: The authors thank Mike Jolly for providing the image in Fig. 3 of the Lorenz manifold computed with the method in [Johnson et al., 1997] and seen from the common viewpoint.

Keywords

unstable manifolds
Lorenz equation
stable manifolds
numerical methods

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2004r14Submitted manuscript, 1.96 MB

http://hdl.handle.net/1983/82

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title = "A survey of methods for computing (un)stable manifolds of vector fields",

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.",

keywords = "unstable manifolds, Lorenz equation, stable manifolds, numerical methods",

author = "B Krauskopf and HM Osinga and EJ Doedel and ME Henderson and J Guckenheimer and A Vladimirsky and M Dellnitz and O Junge",

note = "Additional information: Preprint submitted to the International Journal of Bifurcation and Chaos Sponsorship: The authors thank Mike Jolly for providing the image in Fig. 3 of the Lorenz manifold computed with the method in [Johnson et al., 1997] and seen from the common viewpoint. ",

year = "2004",

language = "English",

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T1 - A survey of methods for computing (un)stable manifolds of vector fields

AU - Krauskopf, B

AU - Osinga, HM

AU - Doedel, EJ

AU - Henderson, ME

AU - Guckenheimer, J

AU - Vladimirsky, A

AU - Dellnitz, M

AU - Junge, O

N1 - Additional information: Preprint submitted to the International Journal of Bifurcation and Chaos Sponsorship: The authors thank Mike Jolly for providing the image in Fig. 3 of the Lorenz manifold computed with the method in [Johnson et al., 1997] and seen from the common viewpoint.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - unstable manifolds

KW - Lorenz equation

KW - stable manifolds

KW - numerical methods

M3 - Working paper

BT - A survey of methods for computing (un)stable manifolds of vector fields

ER -

A survey of methods for computing (un)stable manifolds of vector fields

Abstract

Bibliographical note

Keywords

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