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Title: Normal forms with exponentially small remainder and gevrey normalization for vector fields with a nilpotent linear part
Authors: BONCKAERT, Patrick
Issue Date: 2012
Citation: ANNALES DE L INSTITUT FOURIER, 62 (6), p. 2211-2225
Abstract: We explore the convergence/divergence of the normal form for a singularity of a vector field on C-n with nilpotent linear part. We show that a Gevrey-alpha vector field X with a nilpotent linear part can be reduced to a normal form of Gevrey-1 + alpha type with the use of a Gevrey-1 + alpha transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.
Notes: Bonckaert, P (reprint author), [Bonckaert, Patrick; Verstringe, Freek] Univ Hasselt, B-3590 Diepenbeek, Belgium. Bonckaert, P (reprint author)
URI: http://hdl.handle.net/1942/15013
ISI #: 000316032000007
ISSN: 0373-0956
Category: A1
Type: Journal Contribution
Validation: ecoom, 2014
Appears in Collections: Research publications

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