The number of zeros of Abelian integrals for a perturbation of a hyper-elliptic Hamiltonian system with a nilpotent center and a cuspidal loop

DOI10.14232/ejqtde.2017.1.68zbMath1413.34136OpenAlexW2768602233MaRDI QIDQ4584542

Ali Atabaigi

Publication date: 3 September 2018

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

Full work available at URL: https://doi.org/10.14232/ejqtde.2017.1.68

zbMATH Keywords

limit cycleLiénard equationabelian integralshyper-elliptic Hamiltonian system

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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