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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|
|Publisher: ||ANNALES INST FOURIER|
|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)|
|ISI #: ||000316032000007|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2014|
|Appears in Collections: ||Research publications|
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