Limit cycles bifurcating from the period annulus of quasi-homogeneous centers

DOI10.1007/s10884-008-9126-1zbMath1176.34038OpenAlexW2074022343MaRDI QIDQ1016059

Jaume Llibre, Weigu Li, Jiazhong Yang, Zhi-Fen Zhang

Publication date: 4 May 2009

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-008-9126-1

zbMATH Keywords

bifurcationlimit cycleAbelian integralcyclicitynear-Hamiltonian systemquasi-homogeneous center16th Hilbert's problemhomogeneous center

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (33)

Classification and counting of planar quasi-homogeneous differential systems through their weight vectors ⋮ ON THE DEGENERATE CENTER PROBLEM ⋮ On the centers of the weight-homogeneous polynomial vector fields on the plane ⋮ Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems ⋮ Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems ⋮ Linear type global centers of linear systems with cubic homogeneous nonlinearities ⋮ On the center criterion of planar quasi-homogeneous polynomial differential systems ⋮ Quasi-homogeneous polynomial differential systems having a center at the origin ⋮ On the cyclicity of quasi-homogeneous polynomial systems ⋮ Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems ⋮ Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems ⋮ Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points ⋮ Centers of weight-homogeneous polynomial vector fields on the plane ⋮ Unnamed Item ⋮ Center Problem for Quasi-Homogeneous Polynomial Systems with a Given Weight Degree ⋮ New lower bound for the number of critical periods for planar polynomial systems ⋮ The number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ Center of planar quintic quasi-homogeneous polynomial differential systems ⋮ Structural stability of planar quasihomogeneous vector fields ⋮ Limit cycles bifurcating from planar polynomial quasi-homogeneous centers ⋮ Limit cycles for planar semi-quasi-homogeneous polynomial vector fields ⋮ On the number of critical periods for planar polynomial systems of arbitrary degree ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Global dynamics of planar quasi-homogeneous differential systems ⋮ Unnamed Item ⋮ Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems ⋮ On the cyclicity of weight-homogeneous centers ⋮ Nilpotent Global Centers of Linear Systems with Cubic Homogeneous Nonlinearities ⋮ Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center ⋮ Unnamed Item ⋮ Planar quasi-homogeneous polynomial systems with a given weight degree

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