Integrability of centers perturbed by quasi-homogeneous polynomials
type: Item
instance of: scholarly article
title: Integrability of centers perturbed by quasi-homogeneous polynomials
zbMATH Open document ID: 0876.34008
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-30T00:00:00Z
review text: A polynomial \(X(x,y)\) is called \((p-q)\) quasi-homogeneous of degree \(r\) if the identity \[ X(c^px,c^qy)=c^rX(x,y) \] holds for any real \(c\). The authors consider two-dimensional autonomous systems of the form \[ x'=-y^{2p-1}+X(x,y),\qquad y'=x^{2q-1}+Y(x,y), \] where \(X\) and \(Y\) are \((p-q)\) quasi-homogeneous polynomials of degree \(2pq-q+1\) and \(2pq-p+1\), respectively. Necessary and sufficient conditions for the integrability of this system are given in terms of coefficients of \(X\) and \(Y\).
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1031648
zbMATH Keywords: two-dimensional autonomous systems
zbMATH Keywords: quasi-homogeneous polynomials
zbMATH Keywords: integrability
author: Javier Chavarriga
author: Isaac A. García
author: Jaume Giné
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5402
OpenAlex ID: W2071586795
cites work: Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra
cites work: Integrable systems in the plane with center type linear part
cites work: Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
cites work: Cubic Lienard equations with linear damping
cites work: Stability of motion
DOI: 10.1006/JMAA.1997.5402
description: scientific article; zbMATH DE number 1031648