Global bifurcation of limit cycles in a family of polynomial systems
type: Item
instance of: scholarly article
title: Global bifurcation of limit cycles in a family of polynomial systems
zbMATH Open document ID: 1050.34040
author: Guanghui Xiang
author: Maoan Han
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-10T00:00:00Z
review text: The article is devoted to one of the weakened versions of Hilbert's 16th problem, the so-called infinitesimal Hilbert problem. This task is closely related to the problem of determining an upper bound for the number of limit cycles of the perturbed Hamiltonian system \(\dot{x}=H_y+\varepsilon P(x,y)\), \(\dot{y}=-H_x+\varepsilon Q(x,y)\). The authors give ane stimate on the number of limit cycles for a family of such polynomial systems.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 2085958
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.03.047
OpenAlex ID: W1997495989
cites work: Q4744562
cites work: Cyclicity of a family of vector fields
cites work: On Hopf cyclicity of planar systems
cites work: The Hopf cyclicity of Lienard systems
cites work: Weak focus, limit cycles, and bifurcations for bounded quadratic systems
cites work: Simple exponential estimate for the number of real zeros of complete abelian integrals
cites work: Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
cites work: Q3715459
cites work: Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
DOI: 10.1016/J.JMAA.2004.03.047
Recommended article: On the limit cycle bifurcation of a polynomial system from a global center
Recommended article: GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
Recommended article: Global bifurcation analysis of polynomial dynamical systems
Recommended article: Q5749593
Recommended article: Q3121901
Recommended article: Q4716394
Recommended article: Limit Cycle Bifurcations in a Class of Piecewise Smooth Polynomial Systems
Recommended article: LIMIT CYCLE BIFURCATIONS OF TWO KINDS OF POLYNOMIAL DIFFERENTIAL SYSTEMS
Recommended article: Q3389050
Recommended article: Bifurcation of limit cycles from a polynomial non-global center
description: scientific article; zbMATH DE number 2085958