Symmetries and convergence of normalizing transformations
type: Item
instance of: scholarly article
title: Symmetries and convergence of normalizing transformations
zbMATH Open document ID: 0804.34040
author: S Walcher
author: A. D. Bryuno
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-08-22T00:00:00Z
review text: Normal forms of 2-dimensional systems of autonomous ordinary differential equations are considered in a neighbourhood of a stationary point. It is supposed that the linear part is semisimple, non-zero and the normal form contains infinitely many terms. The author proves the following theorem: The system (under the above conditions) allows a convergent transformation into normal form if and only if it admits a local one- parameter group of symmetries. The paper contains a general discussion, conjectures on existence of convergent normalizing transformations.
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 599917
zbMATH Keywords: normal forms
zbMATH Keywords: local one-parameter group of symmetries
zbMATH Keywords: convergent normalizing transformations
reviewed by: Péter F. Moson
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1163
OpenAlex ID: W2073866908
DOI: 10.1006/JMAA.1994.1163
description: scientific article; zbMATH DE number 599917