A note on higher order Melnikov functions

DOI10.1007/BF02972677zbMath1144.34024OpenAlexW1998171423MaRDI QIDQ2468836

Ahmed Jebrane, Henryk Żołądek

Publication date: 11 February 2008

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02972677

zbMATH Keywords

limit cycleAbelian integralweakened Hilbert's 16th problemdisplacement maphigher-order Melnikov integralPlanar polynomial system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Equivalence of the Melnikov function method and the averaging method ⋮ High-order Melnikov method for time-periodic equations ⋮ Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials ⋮ The number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ Periodic orbits from second order perturbation via rational trigonometric integrals ⋮ Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications

Cites Work

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