The number of limit cycles of a polynomial system on the plane
type: Item
instance of: scholarly article
title: The number of limit cycles of a polynomial system on the plane
zbMATH Open document ID: 1300.34068
DOI: 10.1155/2013/482850
author: Chao Liu
author: Maoan Han
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: The paper is devoted to a perturbed planar system of the form \[ \dot{x}=-yC(x,y) +\varepsilon P(x,y), \quad \dot{y}=xC(x,y)+\varepsilon Q(x,y), \] where \(\varepsilon \) is a small real parameter, \(C(x,y)=(1-y^2)^m\) and \(P(x,y), Q(x,y)\) are real polynomials of degree \(n\). By studying the number of zeros of the corresponding abelian integral the authors estimate the number of limit cycles bifurcating from the period annulus surrounding the origin of the unperturbed planar system.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6306867
zbMATH Keywords: perturbed planar system
zbMATH Keywords: limit cycle
zbMATH Keywords: abelian integral
zbMATH Keywords: 16-th Hilbert's problem
Wikidata QID: Q58916389
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/482850
OpenAlex ID: W2097262626
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description: scientific article; zbMATH DE number 6306867