Linearization of isochronous centers
type: Item
instance of: scholarly article
title: Linearization of isochronous centers
zbMATH Open document ID: 0830.34023
author: Pavao Mardešić
author: Christiane Rousseau
author: Bourama Toni
published in: Journal of Differential Equations
publication date: 1995-09-25T00:00:00Z
review text: The authors propose a unified technique for the study of the isochronicity of polynomial systems. They first construct the linearizing changes of coordinates for isochronous systems having rational first integrals, namely for quadratic systems, for cubic systems symmetric with respect to a center and for reduced Kukles systems. Further, other two classes of systems with isochronous centers having a Darboux first integral are studied, namely cubic systems symmetric with respect to the line and satisfying \(\dot\Theta= 1\) and the class of systems \(\dot z= iP(z)\), for which the authors derive the linearizing changes of coordinates and discuss their geometric properties. Some geometric properties of the linearizing change of coordinates for a system with a rational first integral in the complex plane are discussed and a number of open question for further research is posed.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 800402
zbMATH Keywords: isochronicity
zbMATH Keywords: polynomial systems
zbMATH Keywords: linearizing changes of coordinates
zbMATH Keywords: first integrals
zbMATH Keywords: center
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1122
OpenAlex ID: W2016269254
DOI: 10.1006/JDEQ.1995.1122
description: scientific article; zbMATH DE number 800402