Cyclicity of period annuli and principalization of Bautin ideals

DOI10.1017/S0143385707000971zbMath1172.37020arXiv0705.1112OpenAlexW2962698593MaRDI QIDQ3623582

Lyubomir Gavrilov

Publication date: 21 April 2009

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.1112

zbMATH Keywords

bifurcationlimit cycleplanar vector fieldcyclicityperiod annulus

Mathematics Subject Classification ID

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) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (14)

Medium Amplitude Limit Cycles of Some Classes of Generalized Liénard Systems ⋮ Study of the period function of a two-parameter family of centers ⋮ The limit cycles in a generalized Rayleigh-Liénard oscillator ⋮ The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one ⋮ On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields ⋮ On the limit cycles bifurcating from a quadratic reversible center of genus one ⋮ Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop ⋮ Algebraic and analytical tools for the study of the period function ⋮ On the finite cyclicity of open period annuli ⋮ Principal part of multi-parameter displacement functions ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ Essential perturbations of polynomial vector fields with a period annulus ⋮ Perturbation theory of the quadratic Lotka–Volterra double center ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles

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