Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle

DOI10.1016/j.nonrwa.2015.08.005zbMath1345.34041OpenAlexW1931587871MaRDI QIDQ900637

Jihua Yang, Lincheng Zhao

Publication date: 22 December 2015

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2015.08.005

zbMATH Keywords

abelian integralChebyshev spaceweakened Hilbert's 16th problemPicards-Fuchs equation

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Limit cycle bifurcations of a piecewise smooth Hamiltonian system with a generalized heteroclinic loop through a cusp ⋮ Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\) ⋮ Limit cycle bifurcations for piecewise smooth integrable differential systems ⋮ On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities ⋮ On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems ⋮ The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Upper bounds for the number of zeroes for some abelian integrals
• On the number of zeros of abelian integrals for a kind of quartic Hamiltonians
• Global bifurcation of limit cycles in a family of polynomial systems
• On the number of limit cycles bifurcating from a non-global degenerated center
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Bifurcation of limit cycles from a polynomial non-global center
• On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem
• Quadratic perturbations of quadratic codimension-four centers
• The number of limit cycles of a quintic polynomial system
• 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
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Linear estimate of the number of zeros of abelian integrals for a kind of quintic Hamiltonians
• Linear estimate of the number of zeros of Abelian integrals for a class of integrable non-Hamiltonian systems.
• On the algebraic structure of abelian integrals for a kind of perturbed cubic Hamiltonian systems
• Estimate of the number of zeros of abelian integrals for a kind of quartic Hamiltonians with two centers
• The cyclicity of period annuli of a class of quintic Hamiltonian systems
• Limit cycles of a perturbed cubic polynomial differential center
• Linear estimate of the number of limit cycles for a class of nonlinear systems
• Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics
• An explicit linear estimate for the number of zeros of Abelian integrals
• An improved estimate for the number of zeros of Abelian integrals for cubic Hamiltonians
• Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop
• On the limit cycle bifurcation of a polynomial system from a global center
• Complex zeros of an elliptic integral
• Complex zeros of an elliptic integral
• Averaging analysis of a perturbated quadratic center

This page was built for publication: Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle