An improvement to Darboux integrability theorem for systems having a center

DOI10.1016/S0893-9659(99)00127-5zbMath0978.34022OpenAlexW1968483157MaRDI QIDQ1975316

Javier Chavarriga, Hector J. Giacomini, Jaume Giné

Publication date: 9 April 2000

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(99)00127-5

zbMATH Keywords

Darboux first integralsexponential factorsalgebraic solutions

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Analytic nilpotent centers as limits of nondegenerate centers revisited ⋮ A survey on the inverse integrating factor ⋮ Invariants of polynomial vector fields ⋮ Darboux integrability and the inverse integrating factor. ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ On the linearization of isochronous centre of a modified Emden equation with linear external forcing ⋮ Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields

Cites Work

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• Equations de Pfaff algébriques
• Algebraic invariant curves and the integrability of polynomial systems
• Partial integrals and the first focal value in the problem of centre
• Algebraic solutions for polynomial systems with emphasis in the quadratic case
• Elementary First Integrals of Differential Equations
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Invariant algebraic curves and conditions for a centre

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