Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields

DOI10.1016/j.jde.2015.07.027zbMath1334.34070OpenAlexW1181435521MaRDI QIDQ496752

Haihua Liang, Joan Torregrosa

Publication date: 22 September 2015

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

Full work available at URL: https://doi.org/10.1016/j.jde.2015.07.027

zbMATH Keywords

Lyapunov constantplanar polynomial vector fieldparallelizationcenter cyclicity

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (17)

Lower bounds for the local cyclicity for families of centers ⋮ Bifurcation of 2-periodic orbits from non-hyperbolic fixed points ⋮ The local cyclicity problem: Melnikov method using Lyapunov constants ⋮ Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator ⋮ 24 crossing limit cycles in only one nest for piecewise cubic systems ⋮ Lower bounds for the cyclicity of centers of quadratic three-dimensional systems ⋮ Counting configurations of limit cycles and centers ⋮ Bi-center conditions and local bifurcation of critical periods in a switching \(Z_2\) equivariant cubic system ⋮ Weak-foci of high order and cyclicity ⋮ Lower bounds for the local cyclicity of centers using high order developments and parallelization ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ New lower bounds for the Hilbert numbers using reversible centers ⋮ Local cyclicity in low degree planar piecewise polynomial vector fields ⋮ New lower bounds of the number of critical periods in reversible centers ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields ⋮ Linearizability of planar polynomial Hamiltonian systems ⋮ On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique

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