Higher order Melnikov function for a quartic Hamiltonian with cuspidal loop

DOI10.3934/dcds.2002.8.995zbMath1019.34038OpenAlexW2026181025MaRDI QIDQ1848990

Yulin Zhao, Si-Ming Zhu

Publication date: 8 September 2003

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2002.8.995

zbMATH Keywords

limit cyclecuspidal loopAbelian integralsweakened Hilbert's 16th problem\(k\)th-order Melnikov functionpolynomial Hamiltonian vector field

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) 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 (5)

On the limit cycles of planar polynomial system with non-rational first integral via averaging method at any order ⋮ Limit cycles of a perturbed cubic polynomial differential center ⋮ On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity ⋮ Perturbations of non-Hamiltonian reversible quadratic systems with cubic orbits ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method

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