Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
type: Item
instance of: scholarly article
title: Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
zbMATH Open document ID: 1067.34032
author: Mingqiang Zhang
author: Jibin Li
published in: Journal of Dynamics and Differential Equations
publication date: 2005-02-18T00:00:00Z
review text: The authors consider the weakened Hilbert's 16th problem for symmetric planar perturbed polynomial Hamiltonian systems. They construct an example of such system which is \(Z_8\)-equivariant. By using bifurcation theory of planar polynomial dynamical systems and the method of detection functions, with the help of numerical analysis, the authors show that there exist parameter groups such that the perturbed polynomial Hamiltonian vector field of degree~\(7\) has at least \(7^2=49\) limit cycles with \(Z_8\)~symmetry.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 2134832
zbMATH Keywords: bifurcation
zbMATH Keywords: limit cycle
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: \(Z_8\)-equivariant planar vector field
zbMATH Keywords: weakened Hilbert's 16th problem
MaRDI profile type: Publication
full work available at URL: s10884-004-7835-7
OpenAlex ID: W2787858293
cites work: On the nonexistence, existence and uniqueness of limit cycles
cites work: THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
cites work: Q4279138
cites work: Mathematical problems for the next century
DOI: 10.1007/S10884-004-7835-7
description: scientific article; zbMATH DE number 2134832