Normal forms for vector fields with respect to an arbitrary dilation
type: Item
instance of: scholarly article
title: Normal forms for vector fields with respect to an arbitrary dilation
zbMATH Open document ID: 0856.34042
DOI: 10.1007/BF01194069
author: Fabio Ancona
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1996-09-30T00:00:00Z
review text: The problem of computing normal forms for vector fields having a (possibly degenerate) linear part is considered. The main idea is to consider the given vector field as a perturbation of its homogeneous part of degree one with respect to some dilation \(\delta^r_\varepsilon\). The main result of the paper gives a necessary and sufficient condition for the existence of a local, analytic coordinate change which transforms a real analytic vector field into a homogeneous field of degree greater than or equal to one with respect to a given dilation \(\delta^r_\varepsilon\). An example illustrating how this result can be used to compute a coordinate change which transforms a given field into a homogeneous field of degree one with respect to a dilation \(\delta^r_\varepsilon\) is given.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 929975
zbMATH Keywords: normal forms for vector fields
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01194069
OpenAlex ID: W2040808396
description: scientific article; zbMATH DE number 929975