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

Research output: Working paperWorking paper and Preprints

  • B Krauskopf
  • HM Osinga
  • EJ Doedel
  • ME Henderson
  • J Guckenheimer
  • A Vladimirsky
  • M Dellnitz
  • O Junge
Original languageEnglish
Publication date2004
StateUnpublished

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.

Additional information

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.

Research areas

  • unstable manifolds, Lorenz equation, stable manifolds, numerical methods

Documents

Documents

  • 2004r14

    Preprint (usually an early version) , 1 MB, PDF-document

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