Center conditions for polynomial Liénard systems

DOI10.1007/s12346-016-0202-3zbMath1392.34027OpenAlexW2403163037MaRDI QIDQ1707521

Jaume Giné

Publication date: 3 April 2018

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10459.1/62957

zbMATH Keywords

Gröbner basescenter problemanalytic integrabilitydecomposition in prime idealspolynomial Liénard differential systems

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)

Related Items

Integrability of Liénard systems with a weak saddle ⋮ On the integrability of Liénard systems with a strong saddle ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ Hopf Bifurcation of Z2-Equivariant Generalized Liénard Systems ⋮ Versal unfolding of a nilpotent Liénard equilibrium within the odd Liénard family ⋮ A complete classification on the center-focus problem of a generalized cubic Kukles system with a nilpotent singular point ⋮ Liénard Equation and Its Generalizations ⋮ The application of Liénard transformations to predator-prey systems ⋮ Invariant algebraic curves for certain generalized Liénard differential system ⋮ Center conditions for generalized polynomial Kukles systems ⋮ Center problem for trigonometric Liénard systems ⋮ Bi-center problem and Hopf cyclicity of a cubic Liénard system ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ Center conditions of a particular polynomial differential system with a nilpotent singularity ⋮ Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case ⋮ Algebraic criterion for the existence of a center at a monodromic singular point of a polynomial Liénard system ⋮ Nondegenerate centers for Abel polynomial differential equations of second kind

Uses Software

• SINGULAR
• primdec

Cites Work

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• SINGULAR