The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point

DOI10.1016/j.amc.2014.01.006zbMath1410.34096OpenAlexW1982704724MaRDI QIDQ1644531

Yulin Zhao, Yanyan Chen

Publication date: 21 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.01.006

zbMATH Keywords

limit cycleabelian integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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)

Related Items (2)

A class of quadratic reversible systems with a center of genus one ⋮ Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

Cites Work

• The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one
• On the period function of reversible quadratic centers with their orbits inside quartics
• 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
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• Quadratic perturbations of quadratic codimension-four centers
• On the number of critical points of the period
• Remark on the number of critical points of the period
• Quadratic systems with center and their perturbations
• On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
• Perturbations of quadratic centers
• Abelian integrals for cubic vector fields
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
• Qualitative theory of planar differential systems
• A Chebyshev criterion for Abelian integrals
• On the number of limit cycles in quadratic perturbations of quadratic codimension-four centres
• Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops
• The infinitesimal 16th Hilbert problem in the quadratic case
• Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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