\(C^\infty\)-normal forms of local vector fields
type: Item
instance of: scholarly article
title: \(C^\infty\)-normal forms of local vector fields
zbMATH Open document ID: 1011.34026
DOI: 10.1023/A:1013909812387
published in: Acta Applicandae Mathematicae
publication date: 2002-05-30T00:00:00Z
review text: It is well known that a resonant normal form and a normalizing transformation are not uniquely determined. This fact can be used for a further simplification of a normal form (the so-called ``secondary'' normalization). Here, a direct definition of a secondary normalization is given. In contrast with a traditional normalization, a secondary normalization turns out to be uniquely determined for formally equivalent systems. As follows from examples treated in the paper, at least in the case of low dimensions the secondary normalization leads to the most simple formal system a given system can be brought to. As a rule, even for analytic systems formal normalizing transformations diverge. However, as shown in the paper, these transformations in certain cases correspond to \(C^{\infty}\)-smooth changes of variables.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 58K50
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 1747773
zbMATH Keywords: vector field
zbMATH Keywords: conjugacy
zbMATH Keywords: normal form
zbMATH Keywords: formal normal form
zbMATH Keywords: formal conjugacy
zbMATH Keywords: linearization
author: G. Belitskii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1747773