Perturbation theory of a symmetric center within Liénard equations

DOI10.1016/j.jde.2015.03.039zbMath1387.34088OpenAlexW2034788479MaRDI QIDQ2347820

Dongmei Xiao, Jean-Pierre Françoise

Publication date: 9 June 2015

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

Full work available at URL: https://doi.org/10.1016/j.jde.2015.03.039

zbMATH Keywords

Liénard systemsLambert functionAbelian integrals

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) 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)

Related Items (12)

Studies of the Petrov module for a family of generalized Liénard integrable systems ⋮ On the Chebyshev property of certain abelian integrals near a polycycle ⋮ On the positive periodic solutions of a class of Liénard equations with repulsive singularities in degenerate case ⋮ On the indices of singular points for planar bounded piecewise smooth polynomial vector field ⋮ Bifurcations of traveling wave solutions of a generalized Burgers-Fisher equation ⋮ A proof of a Dumortier-Roussarie's conjecture ⋮ Bifurcation and dynamics of periodic solutions to the Rayleigh-plesset equation: theory and numerical simulation ⋮ The number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order ⋮ Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center ⋮ Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ New family of abelian integrals satisfying Chebyshev property

Cites Work

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