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http://hdl.handle.net/1942/15013
Title: | Normal forms with exponentially small remainder and gevrey normalization for vector fields with a nilpotent linear part | Authors: | BONCKAERT, Patrick VERSTRINGE, Freek |
Issue Date: | 2012 | Publisher: | ANNALES INST FOURIER | Source: | 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) | Keywords: | normal forms; nilpotent linear part; representation theory; Gevrey normalization;Mathematics; normal forms; nilpotent linear part; representation theory; Gevrey normalization | Document URI: | http://hdl.handle.net/1942/15013 | ISSN: | 0373-0956 | e-ISSN: | 1777-5310 | ISI #: | 000316032000007 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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