The center problem for a linear center perturbed by homogeneous polynomials
type: Item
instance of: scholarly article
title: The center problem for a linear center perturbed by homogeneous polynomials
zbMATH Open document ID: 1124.34326
author: Jaume Giné
publication date: 2007-05-24T00:00:00Z
review text: The author studies the center problem for a special system of differential equations of the form \[ \dot x=-y+X_{s}(x,y),\qquad \dot y=x+Y_{s}(x,y), \] where \(X_{s}(x,y)\) and \(Y_{s}(x,y)\) are homogeneous polynomials of degree \(s,\) with \(s\geq2.\) It is known that the centers of the polynomial differential systems with a linear center perturbed by homogeneous polynomials have been studied for the degrees \(s=2,3,4,5\); they are completely classified for \(s=2,3\) and partially classified for \(s=4,5.\) The author recalls these results and gives new centers for \(s=6,7.\)
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5156854
zbMATH Keywords: system of polynomial differential equations
zbMATH Keywords: center problem
MaRDI profile type: Publication
full work available at URL: s10114-005-0623-4
OpenAlex ID: W2129935427
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DOI: 10.1007/S10114-005-0623-4
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5156854