Obstacles to local smooth linearization of systems of ordinary differential equations
type: Item
instance of: scholarly article
title: Obstacles to local smooth linearization of systems of ordinary differential equations
zbMATH Open document ID: 0851.34007
DOI: 10.1007/BF02304566
author: V. S. Samovol
published in: Mathematical Notes
publication date: 1996-11-26T00:00:00Z
review text: The paper is devoted to the problem of the existence of a nondegenerate invariable diffeomorphism \(\xi= H(\eta)\) of the class \(C^k\), \(k\geq 1\), which reduces the system \(\dot\xi= A\xi+ F(\xi)\), \(|F(\xi)|= o(|\xi|)\) into the linear system \(\dot\eta=A \eta\). For the system \(\dot x= x\), \(\dot y= 2y\), \(\dot z= -z\), \(\dot w= 2w+ xy^2 z^3\) it is shown that \(k= 2\) is the greatest value for which such a diffeomorphism exists.
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 898902
zbMATH Keywords: local smooth linearization
zbMATH Keywords: diffeomorphism
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
cites work: Q5616341
description: scientific article; zbMATH DE number 898902