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

AUTHORS: 

Inmaculada Baldoma

Departament d'Enginyeria Informatica i Matematiques
Universitat Rovira i Virgili
Campus Sescelades. Avinguda dels Paisos Catalans 26
47003, Tarragona, Spain

Ernest Fontich

Departament de Matematica Aplicada i Analisi
Universitat de Barcelona
Gran Via 585. 08007 Barcelona. Spain


Rafael de la Llave

Department of Mathematics, 1 University Station C1200
The University of Texas at Austin
Austin, TX 78712-1082, U.S.A

Pau Martin

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


E-mails: immaculada.baldoma@upc.edu, fontich@ub.edu, llave@math.utexas.edu, martin@ma4.upc.edu

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.