Finite smooth normal forms and integrability of local families of vector fields
type: Item
instance of: scholarly article
title: Finite smooth normal forms and integrability of local families of vector fields
zbMATH Open document ID: 1216.37014
author: Vincent Naudot
author: Jiazhong Yang
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2011-01-19T00:00:00Z
review text: From the authors' abstract: A class of smooth vector fields which depend on small parameters and whose eigenvalues may admit certain resonances are studied. Polynomial normal forms for such systems under \(C^k\) conjugacy, where \(k\) can be arbitrarily large, are considered. When the smoothness of normalization is less required, it is showed that these systems can be reduced to their quasi-linearizable normal forms under \(C^{k_0}\) conjugacy, where \(k_0\) is good enough to preserve certain qualitative properties of the original systems while the normal forms are as convenient as the linearized ones in applications.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37E30
zbMATH DE Number: 5838576
zbMATH Keywords: normal form
zbMATH Keywords: strongly 1-resonant condition
zbMATH Keywords: tagged monomial function
zbMATH Keywords: tagged function
zbMATH Keywords: logarithmic Mourtada type function
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: dcdss.2010.3.667
OpenAlex ID: W2329035950
DOI: 10.3934/DCDSS.2010.3.667
description: scientific article; zbMATH DE number 5838576