Compactification and desingularization of spaces of polynomial Liénard equations
type: Item
instance of: scholarly article
title: Compactification and desingularization of spaces of polynomial Liénard equations
zbMATH Open document ID: 1105.34015
author: Freddy Dumortier
published in: Journal of Differential Equations
publication date: 2006-06-09T00:00:00Z
review text: This interesting paper presents a good compactification for all spaces of polynomial Liénard systems \[ \dot{x}=y, \qquad \dot{y}=-g(x)-yf(x) \] with \(g(x)\) and \(f(x)\) polynomials of degrees \(m\) and \(n\), respectively. The author shows that it is possible to compactify and desingularize the space of such system for each \((m,n)\) separately by using both Hamiltonian and singular perturbations.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 5030966
zbMATH Keywords: Liénard equation
zbMATH Keywords: Hilbert's 16th problem
zbMATH Keywords: limit cycle
zbMATH Keywords: compactification
zbMATH Keywords: desingularization
zbMATH Keywords: Hamiltonian perturbation
zbMATH Keywords: singular perturbation
MaRDI profile type: Publication
full work available at URL: j.jde.2005.08.011
OpenAlex ID: W2018800950
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cites work: Q3831770
cites work: Putting a boundary to the space of Liénard equations
cites work: Mathematical problems for the next century
DOI: 10.1016/J.JDE.2005.08.011
description: scientific article