On the algebraic structure of abelian integrals for a kind of perturbed cubic Hamiltonian systems

DOI10.1016/j.jmaa.2009.05.034zbMath1180.34033OpenAlexW1984916261MaRDI QIDQ2272041

Yanyan Li

Publication date: 5 August 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.05.034

zbMATH Keywords

Picard-Fuchs equationabelian integralweakened Hilbert's 16th problemcubic Hamiltonian system

Mathematics Subject Classification ID

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 (8)

Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities ⋮ Limit cycle bifurcations by perturbing a class of planar quintic vector fields ⋮ The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points ⋮ On the number of zeros of abelian integral for a class of cubic Hamilton systems with the phase portrait ``butterfly ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems ⋮ The study on cyclicity of a class of cubic systems ⋮ The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

Cites Work

• A unified proof of the weakened Hilbert 16th problem for \(n=2\)
• Number of zeros of complete elliptic integrals
• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• Elliptic integrals and their nonoscillation
• Zeroes of complete elliptic integrals for 1:2 resonance
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
• Remarks on 16th weak Hilbert problem forn 2*
• Complex zeros of an elliptic integral
• Complex zeros of an elliptic integral
• The infinitesimal 16th Hilbert problem in the quadratic case
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