Limit cycles bifurcating from planar polynomial quasi-homogeneous centers
type: Item
instance of: scholarly article
title: Limit cycles bifurcating from planar polynomial quasi-homogeneous centers
zbMATH Open document ID: 1332.34066
author: Jaume Giné
author: Maite Grau
author: Jaume Llibre
published in: Journal of Differential Equations
publication date: 2015-09-30T00:00:00Z
review text: This paper concerns the following one-parameter family of systems \[ \begin{aligned} & \dot{x}=P(x,y)+ \varepsilon \bar{P}(x,y), \\ & \dot{y}=Q(x,y)+ \varepsilon \bar{Q}(x,y), \end{aligned} \] where \(\varepsilon \neq 0\) is a sufficiently small real perturbation parameter, \(\bar{P}\) and \(\bar{Q}\) are arbitrary real polynomials of degree \(n\). By applying the first order averaging method the authors obtain an upper bound for the maximum number of limit cycles bifurcating from the periodic orbits of any planar polynomial quasi-homogeneous center of the mentioned system.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 6487581
zbMATH Keywords: quasi-homogeneous polynomial differential equation
zbMATH Keywords: bifurcation of limit cycle
zbMATH Keywords: quasi-homogeneous center
MaRDI profile type: Publication
full work available at URL: j.jde.2015.08.014
OpenAlex ID: W1841872528
cites work: Planar quasi-homogeneous polynomial differential systems and their integrability
cites work: On the cyclicity of weight-homogeneous centers
cites work: Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems
cites work: Averaging theory at any order for computing periodic orbits
cites work: Integrability and nonintegrability of dynamical systems
cites work: Cubic homogeneous polynomial centers
cites work: Limit cycles bifurcating from the period annulus of quasi-homogeneous centers
DOI: 10.1016/J.JDE.2015.08.014
description: scientific article; zbMATH DE number 6487581