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2007, Volume 17, Issue 4: 835-865. Doi: 10.3934/dcds.2007.17.835
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The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points

  • 1.

    Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Campus Sescelades. Avinguda dels Pa¨ısos Catalans 26, 47003, Tarragona

  • 2.

    Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona

  • 3.

    School of Mathematics, Georgia Institute of Technology, 686 Cherry St., Atlanta, GA 30332-0160

  • 4.

    Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Ed-C3, Jordi Girona, 1-3, 08034 Barcelona

Received:  June 30, 2005
Revised:  October 31, 2006
Published:  September 2007
Abstract Related Papers Cited by
    Abstract
  • We use the parameterization method to prove the existence and properties of one-dimensional submanifolds of the center manifold associated to the fixed point of $C^r$ maps with linear part equal to the identity. We also provide some numerical experiments to test the method in these cases.
    Mathematics Subject Classification: Primary: 37D10; Secondary: 37N05.

    Citation:
    shu

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