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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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File | Description | Size | Format | |
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jdde1332-normalforms-revision.pdf | Non Peer-reviewed author version | 408.25 kB | Adobe PDF | View/Open |
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