Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8349
Title: Gevrey normal forms of vector fields with one zero eigenvalue
Authors: BONCKAERT, Patrick 
DE MAESSCHALCK, Peter 
Issue Date: 2008
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 344(1). p. 301-321
Abstract: We study normal forms of isolated singularities of vector fields in R-n or C-n. When all eigenvalues of the linear part of the vector field are nonzero, one can eliminate all so-called nonresonant terms from the equation provided some spectral condition (like Siegel) is satisfied. In this paper, we discuss the case where there is one zero eigenvalue (in that case Siegel's condition is not satisfied), and show that the formal normalizing transformations are either convergent or divergent of at most Gevrey type. In some cases, we show the summability of the normalizing transformations, which leads to the existence of analytic normal forms in complex sectors around the singularity. (C) 2008 Elsevier Inc. All rights reserved.
Notes: Hasselt Univ, B-3590 Diepenbeek, Belgium.
Keywords: normal forms; resonances; Gevrey series; summability; Borel-; Laplace transform
Document URI: http://hdl.handle.net/1942/8349
ISSN: 0022-247X
e-ISSN: 1096-0813
DOI: 10.1016/j.jmaa.2008.02.060
ISI #: 000256278500022
Category: A1
Type: Journal Contribution
Validations: ecoom 2009
Appears in Collections:Research publications

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