The parameterization method for center manifolds

Jan Bouwe van den Berg, Wouter Hetebrij, Bob Rink*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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Abstract

In this paper, we present a generalization of the parameterization method, introduced by Cabré, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we find a new proof for the existence and regularity of center manifolds. However, in contrast to the classical center manifold theorem, our parameterization method will simultaneously obtain the center manifold and its conjugate center dynamical system. Furthermore, we will provide bounds on the error between approximations of the center manifold and the actual center manifold, as well as bounds for the error in the conjugate dynamical system.

Original languageEnglish
Pages (from-to)2132-2184
Number of pages53
JournalJournal of Differential Equations
Volume269
Issue number3
Early online date7 Feb 2020
DOIs
Publication statusPublished - 15 Jul 2020

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