On convergent normal from transformations in presence of symmetries
type: Item
instance of: scholarly article
title: On convergent normal from transformations in presence of symmetries
zbMATH Open document ID: 0959.34030
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-26T00:00:00Z
review text: The author proves a convergence criterion for transformations to (Poincaré-Dulac) normal form, which is a generalization of a theorem on the convergence of normalizing transformations in the presence of symmetries due to \textit{G. Cicogna} [J. Math. Anal. Appl. 199, No. 1, 243-255 (1996; Zbl 0855.34042)]. This last theorem extends results of \textit{L. M. Markhashov} [J. Appl. Math. Mech. 38, 738-740 (1975; Zbl 0359.34006)] and \textit{A. D. Bruno} and \textit{S. Walcher} [J. Math. Anal. Appl. 183, No. 3, 571-576 (1994; Zbl 0804.34040)]. On the other hand, the author also shows that the imposed technical hypotheses allow to carry out a computational verification in several classes of vector fields.
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 1441384
zbMATH Keywords: normal forms
zbMATH Keywords: normalizing transformations
zbMATH Keywords: convergence
zbMATH Keywords: centralizer of vector fields
author: S Walcher
reviewed by: Nácere Hayek
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6681
OpenAlex ID: W1993223884
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DOI: 10.1006/JMAA.1999.6681
description: scientific article; zbMATH DE number 1441384