The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points

DOI10.1016/j.jde.2017.06.027zbMath1411.34047OpenAlexW2726863439MaRDI QIDQ1785930

Jihua Yang, Lincheng Zhao

Publication date: 2 October 2018

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

Full work available at URL: https://doi.org/10.1016/j.jde.2017.06.027

zbMATH Keywords

Hamiltonian systemPicard-Fuchs equationabelian integralChebyshev spaceweakened Hilbert's 16th problem

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (13)

Periodic wave solution of the generalized Burgers-Fisher equation via abelian integral ⋮ Limit Cycles Bifurcating from a Class of Cubic Hamiltonian Systems ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis ⋮ Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point ⋮ Global existence and uniqueness of a periodic wave solution of the generalized Burgers-Fisher equation ⋮ Limit cycle bifurcations by perturbing a class of planar quintic vector fields ⋮ On the number of zeros of abelian integral for a class of cubic Hamilton systems with the phase portrait ``butterfly ⋮ Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines ⋮ The study on cyclicity of a class of cubic systems ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system ⋮ Perturbation of a period annulus with a unique two-saddle cycle in higher order Hamiltonian

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