Alien limit cycles in Liénard equations

DOI10.1016/j.jde.2012.11.005zbMath1262.34036OpenAlexW1967680978MaRDI QIDQ1932450

Freddy Dumortier, Rafel Prohens, Bartomeu Coll

Publication date: 18 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.11.005

zbMATH Keywords

limit cycleLiénard equationplanar vector fieldsabelian integralHamiltonian perturbationtwo-saddle cycle

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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