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

B. Krauskopf; H. M. Osinga; E. J. Doedel; M. E. Henderson; J. Guckenheimer; A. Vladimirsky; M. Dellnitz; O. Junge

doi:10.1142/9789812774569_0004

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

B. Krauskopf
, H. M. Osinga
, E. J. Doedel
, M. E. Henderson
, J. Guckenheimer
, A. Vladimirsky
, M. Dellnitz
, O. Junge

University of Bristol
Concordia University
IBM Research
Cornell University
Universität Paderborn

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

9 Scopus citations

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
Title of host publication	Modeling and Computations in Dynamical Systems
Subtitle of host publication	In Commemoration of the 100th Anniversary of the Birth of John von Neumann
Publisher	World Scientific Publishing Co.
Pages	67-95
Number of pages	29
ISBN (Electronic)	9789812774569
ISBN (Print)	9812565965
DOIs	https://doi.org/10.1142/9789812774569_0004
State	Published - 1 Jan 2006
Externally published	Yes

Keywords

Lorenz equations
Stable and unstable manifolds
numerical methods

Access to Document

10.1142/9789812774569_0004

Cite this

Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer, J., Vladimirsky, A., Dellnitz, M., & Junge, O. (2006). A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS. In Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann (pp. 67-95). World Scientific Publishing Co.. https://doi.org/10.1142/9789812774569_0004

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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.",

keywords = "Lorenz equations, Stable and unstable manifolds, numerical methods",

author = "B. Krauskopf and Osinga, \{H. M.\} and Doedel, \{E. J.\} and Henderson, \{M. E.\} and J. Guckenheimer and A. Vladimirsky and M. Dellnitz and O. Junge",

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month = jan,

day = "1",

doi = "10.1142/9789812774569\_0004",

language = "English",

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}

Krauskopf, B, Osinga, HM, Doedel, EJ, Henderson, ME, Guckenheimer, J, Vladimirsky, A, Dellnitz, M & Junge, O 2006, A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS. in Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann. World Scientific Publishing Co., pp. 67-95. https://doi.org/10.1142/9789812774569_0004

A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS. / Krauskopf, B.; Osinga, H. M.; Doedel, E. J. et al.
Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann. World Scientific Publishing Co., 2006. p. 67-95.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS

AU - Krauskopf, B.

AU - Osinga, H. M.

AU - Doedel, E. J.

AU - Henderson, M. E.

AU - Guckenheimer, J.

AU - Vladimirsky, A.

AU - Dellnitz, M.

AU - Junge, O.

PY - 2006/1/1

Y1 - 2006/1/1

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 - Lorenz equations

KW - Stable and unstable manifolds

KW - numerical methods

UR - https://www.scopus.com/pages/publications/85086891597

U2 - 10.1142/9789812774569_0004

DO - 10.1142/9789812774569_0004

M3 - Chapter

AN - SCOPUS:85086891597

SN - 9812565965

SP - 67

EP - 95

BT - Modeling and Computations in Dynamical Systems

PB - World Scientific Publishing Co.

ER -

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

Abstract

Keywords

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