Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11635
 Title: Well adapted normal linearization in singular perturbation problems Authors: BONCKAERT, Patrick DE MAESSCHALCK, Peter DUMORTIER, Freddy Issue Date: 2011 Publisher: Springer Source: Journal of Dynamics and Differential Equations, 23(1). p. 115-139 Abstract: We provide smooth local normal forms near singularities that appear in planar singular perturbation problems after application of the well-known family blow up technique. The local normal forms preserve the structure that is provided by the blow-up ransformation. In a similar context, C^k-structure-preserving normal forms were shown to exist, for any finite k. In this paper, we improve the smoothness by showing the existence of a C^\infty normalizing transformation, or in other cases by showing the existence of a single normalizing transformation that is C^k for each k, provided one restricts the singular parameter epsilon to a (k-dependent) suffiiently small neighborhood of the origin. Keywords: smooth normal linearization, vector field, line of singularities, singular perturbations Document URI: http://hdl.handle.net/1942/11635 ISSN: 1040-7294 e-ISSN: 1572-9222 DOI: 10.1007/s10884-010-9191-0 ISI #: 000290757300005 Category: A1 Type: Journal Contribution Validations: ecoom 2012 Appears in Collections: Research publications

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