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

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

doi:10.1142/S0218127405012533

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

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

Department of Engineering Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

237 Citations (Scopus)

Abstract

The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global table 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.

Translated title of the contribution	A survey of methods for computing (un)stable manifolds of vector fields
Original language	English
Pages (from-to)	763 - 791
Number of pages	29
Journal	International Journal of Bifurcation and Chaos
Volume	15 (3)
DOIs	https://doi.org/10.1142/S0218127405012533
Publication status	Published - Mar 2005

Bibliographical note

Publisher: World Scientific Publ Co Pte Ltd
Other: Also appeared in EJ Doedel, G Domokos & IG Kevrekidis (Eds), Modelling & Computations in Dynamical Systems, World Scientific Series on Nonlinear Science B13 (2006) featured on the cover!

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http://www.worldscinet.com/ijbc/15/preserved-docs/1503/S0218127405012533.pdf

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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 table 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.",

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

note = "Publisher: World Scientific Publ Co Pte Ltd Other: Also appeared in EJ Doedel, G Domokos & IG Kevrekidis (Eds), Modelling & Computations in Dynamical Systems, World Scientific Series on Nonlinear Science B13 (2006) featured on the cover!",

year = "2005",

month = mar,

doi = "10.1142/S0218127405012533",

language = "English",

volume = "15 (3)",

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journal = "International Journal of Bifurcation and Chaos",

issn = "1793-6551",

publisher = "World Scientific Publishing Co.",

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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, JM

AU - Vladimirsky, A

AU - Dellnitz, M

AU - Junge, O

N1 - Publisher: World Scientific Publ Co Pte Ltd Other: Also appeared in EJ Doedel, G Domokos & IG Kevrekidis (Eds), Modelling & Computations in Dynamical Systems, World Scientific Series on Nonlinear Science B13 (2006) featured on the cover!

PY - 2005/3

Y1 - 2005/3

N2 - The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global table 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 table 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.

U2 - 10.1142/S0218127405012533

DO - 10.1142/S0218127405012533

M3 - Article (Academic Journal)

SN - 1793-6551

VL - 15 (3)

SP - 763

EP - 791

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

ER -

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

Abstract

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