Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop

DOI10.1088/0951-7715/16/3/319zbMath1037.34026OpenAlexW2046371282MaRDI QIDQ4430694

Changjian Liu

Publication date: 12 October 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/16/3/319

zbMATH Keywords

Abelian integralelliptic Hamiltonianfigure-of-eight loop

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)

Related Items (12)

Cubic perturbations of elliptic Hamiltonian vector fields of degree three ⋮ On the cubic perturbations of the symmetric 8-loop Hamiltonian ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ The cyclicity of period annuli of a class of quintic Hamiltonian systems ⋮ Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain ⋮ On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity ⋮ The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points ⋮ Perturbations from a kind of quartic Hamiltonians under general cubic polynomials ⋮ The monotonicity of the ratio of two Abelian integrals ⋮ Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain ⋮ A new Chebyshev criterion and its application to planar differential systems ⋮ The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

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