Integrability of centers perturbed by quasi-homogeneous polynomials

DOI10.1006/jmaa.1997.5402zbMath0876.34008OpenAlexW2071586795MaRDI QIDQ1359667

Jaume Giné, Javier Chavarriga, Isaac A. García

Publication date: 30 October 1997

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5402

zbMATH Keywords

integrabilitytwo-dimensional autonomous systemsquasi-homogeneous polynomials

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34)

Related Items (16)

Two kinds of bifurcation phenomena in a quartic system ⋮ Bifurcation of limit cycles in a quintic system with ten parameters ⋮ Local bifurcation of limit cycles and integrability of a class of nilpotent systems ⋮ Centers of quasi-homogeneous polynomial planar systems ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov system ⋮ Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems ⋮ Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ A note on analytic integrability of planar vector fields ⋮ BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM ⋮ Reversibility and quasi-homogeneous normal forms of vector fields ⋮ Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov system ⋮ Center conditions of a particular polynomial differential system with a nilpotent singularity ⋮ On orbital-reversibility for a class of planar dynamical systems ⋮ Center problem for several differential equations via Cherkas' method

Cites Work

• Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra
• Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
• Stability of motion
• Cubic Lienard equations with linear damping
• Integrable systems in the plane with center type linear part

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