On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields

DOI10.1007/s10688-013-0024-xzbMath1310.34043arXiv1106.0857OpenAlexW2075903958MaRDI QIDQ482557

Lyubomir Gavrilov

Publication date: 5 January 2015

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0857

zbMATH Keywords

limit cyclesheteroclinic loopfinite cyclicitytwo-saddle loop

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (7)

Cubic perturbations of elliptic Hamiltonian vector fields of degree three ⋮ The limit cycles in a generalized Rayleigh-Liénard oscillator ⋮ Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems ⋮ Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop ⋮ Bifurcation of the separatrix skeleton in some 1-parameter families of planar vector fields ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles ⋮ Cyclicity of canard cycles with hyperbolic saddles located away from the critical curve

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