The role of algebraic solutions in planar polynomial differential systems

DOI10.1017/S0305004107000497zbMath1136.34036arXivmath/0506036OpenAlexW3098422168MaRDI QIDQ5428393

Maite Grau, Hector J. Giacomini, Jaume Giné

Publication date: 22 November 2007

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506036

zbMATH Keywords

invariant algebraic curveDarboux functionfirst integralintegrating factorcofactoralgebraic particular solution

Mathematics Subject Classification ID

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

Related Items (4)

Classifying algebraic invariants and algebraically invariant solutions ⋮ Invariant algebraic curves for Liénard dynamical systems revisited ⋮ Integrable geodesic flows and metrisable second-order ordinary differential equations ⋮ Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

Cites Work

• Darboux integrability and the inverse integrating factor.
• Generalized cofactors and nonlinear superposition principles
• Simple Darboux points of polynomial planar vector fields.
• Elementary First Integrals of Differential Equations
• An algorithmic method to determine integrability for polynomial planar vector fields
• Liouvillian First Integrals of Differential Equations
• Invariant algebraic curves and conditions for a centre
• About a conjecture on quadratic vector fields

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