The cyclicity of period annuli of a class of quintic Hamiltonian systems

DOI10.1016/j.jmaa.2013.02.016zbMath1288.34033OpenAlexW2001070781MaRDI QIDQ2442975

Minghui Qi, Changjian Liu, Lincheng Zhao

Publication date: 2 April 2014

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.2013.02.016

zbMATH Keywords

abelian integralhyper-elliptic Hamiltonian systemcyclicity of period annuli

Mathematics Subject Classification ID

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

Related Items (15)

The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ The perturbation of a class of hyper-elliptic Hamilton system with a double eight figure loop ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle ⋮ Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials ⋮ 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 limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations ⋮ A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE ⋮ Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system

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