The cyclicity of period annuli of a class of quadratic reversible systems with two centers

DOI10.1016/j.jde.2012.02.005zbMath1244.34049OpenAlexW2034325162MaRDI QIDQ414811

Changjian Liu

Publication date: 11 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.02.005

zbMATH Keywords

limit cyclesmall perturbationabelian integralsquadratic reversible centers

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (13)

Normal forms for equivariant differential equations ⋮ On the fixed points set of differential systems reversibilities ⋮ The cyclicity of a class of quadratic reversible centers defining elliptic curves ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems ⋮ Every period annulus is both reversible and symmetric ⋮ Quadratic double centers and their perturbations ⋮ Limit cycles appearing from a generalized heteroclinic loop with a cusp and a nilpotent saddle ⋮ The Number of Limit Cycles Bifurcating from a Quadratic Reversible Center ⋮ Bi-center problem and Hopf cyclicity of a cubic Liénard system ⋮ Abelian integrals and limit cycles for a class of cubic polynomial vector fields of Lotka-Volterra type with a rational first integral of degree two ⋮ Periodic orbits from second order perturbation via rational trigonometric integrals ⋮ Centers with equal period functions

Cites Work

• Unnamed Item
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• The cyclicity of the period annulus of a quadratic reversible system with a hemicycle
• Bifurcation of limit cycles from quadratic isochrones
• A unified proof of the weakened Hilbert 16th problem for \(n=2\)
• Perturbations of quadratic centers of genus one
• The cyclicity of period annuli of some classes of reversible quadratic systems
• Quadratic centers defining elliptic surfaces
• Quadratic perturbations of a class of quadratic reversible systems with one center
• Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
• Quadratic perturbations of a class of quadratic reversible systems with two centers
• Elliptic integrals and their nonoscillation
• Cyclicity of infinite contour around certain reversible quadratic center
• Quadratic systems with center and their perturbations
• Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops
• Perturbations of quadratic centers
• On the distribution and number of limit cycles for quadratic systems with two foci
• Unfolding of a quadratic integrable system with a homoclinic loop
• Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop
• Two-dimensional Fuchsian systems and the Chebyshev property.
• Limit cycles bifurcated from a reversible quadratic center
• A Chebyshev criterion for Abelian integrals
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
• Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops
• Remarks on 16th weak Hilbert problem forn 2*
• Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop
• Abelian integrals and limit cycles
• The infinitesimal 16th Hilbert problem in the quadratic case

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