American Institute of Mathematical Sciences

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October  2007, 17(4): 835-865. doi: 10.3934/dcds.2007.17.835

The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points

Inmaculada Baldomá 1, , Ernest Fontich 2, , Rafael de la Llave 3, and  Pau Martín 4,

1. 

Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Campus Sescelades. Avinguda dels Pa¨ısos Catalans 26, 47003, Tarragona, Spain
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, United States
4. 

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

Received  July 2005 Revised  November 2006 Published  January 2007

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.
Keywords: Parabolic point, parameterization method., invariant manifold.
Mathematics Subject Classification: Primary: 37D10; Secondary: 37N0.
Citation: Inmaculada Baldomá, Ernest Fontich, Rafael de la Llave, Pau Martín. The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 835-865. doi: 10.3934/dcds.2007.17.835
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