On the number of limit cycles for perturbed pendulum equations

DOI10.1016/j.jde.2016.04.025zbMath1346.34029arXiv1602.00617OpenAlexW2267985152MaRDI QIDQ285654

Anna Geyer, Armengol Gasull, Francesc Mañosas

Publication date: 19 May 2016

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

Full work available at URL: https://arxiv.org/abs/1602.00617

zbMATH Keywords

limit cyclesabelian integralsinfinitesimal sixteenth Hilbert problemperturbed pendulum equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) 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)

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