Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system
type: Item
instance of: scholarly article
title: Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system
zbMATH Open document ID: 1214.34025
author: Heilong Mi
author: Chaoxiong Du
author: Yirong Liu
publication date: 2010-11-17T00:00:00Z
review text: The authors study limit cycle bifurcations of four fine foci in a \(Z_4\)-equivariant quintic system and the problem when its four singular points can be centers and isochronous centers at the same time.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 37G40
zbMATH DE Number: 5816560
zbMATH Keywords: \(Z_4\)-equivariant quintic system
zbMATH Keywords: focal value
zbMATH Keywords: center
zbMATH Keywords: isochronous center
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: s10114-010-7541-9
OpenAlex ID: W1977071188
cites work: HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
cites work: REDUCE and the bifurcation of limit cycles
cites work: Theory of values of singular point in complex autonomous differential systems
cites work: Theory of center-focus for a class of higher-degree critical points and infinite points
cites work: Q3868118
cites work: On hereditarily indecomposable Banach spaces
cites work: Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
cites work: A cubic system with twelve small amplitude limit cycles
cites work: Small limit cycles bifurcating from fine focus points in quartic order \(Z_{3}\)-equivariant vector fields
cites work: Bifurcations of the limit cycles in a \(z_3\)-equivariant quartic planar vector field
cites work: Analysis on limit cycles of \(Z_{q}\)-equivariant polynomial vector fields with degree 3 or 4
cites work: Q4715040
cites work: Conditions for the existence of a center for the Kukles homogeneous systems
cites work: Center conditions for a lopsided quartic polynomial vector field
cites work: Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial
cites work: Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials
cites work: Q5513883
cites work: Q5665494
cites work: A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS
cites work: A new method to determine isochronous center conditions for polynomial differential systems.
DOI: 10.1007/S10114-010-7541-9
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5816560