About algebraic integrability and non-integrability of ordinary differential equations

DOI10.1016/S0960-0779(97)00048-9zbMath0935.34029OpenAlexW2050549718WikidataQ104405205 ScholiaQ104405205MaRDI QIDQ1963227

Andrzej J. Maciejewski

Publication date: 24 January 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(97)00048-9

zbMATH Keywords

nonintegrabilityalgebraic integrabilitycompatible vector fieldsLagutinskii-Levelt method

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (6)

The characteristic function method of finding first integrals of ODEs ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ A generalization of the Lax equation ⋮ Painlevé analysis and integrable cases of coupled cubic oscillators in the plane. ⋮ Invariants of homogeneous ordinary differential equations ⋮ New classes of quadratic vector fields admitting integral-preserving Kahan–Hirota–Kimura discretizations

Cites Work

• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• Equations de Pfaff algébriques
• M. N. Lagutinskij (1871-1915): A misunderstood mathematician
• Integrability, computation and applications
• On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development
• On the nonexistence of rational first integrals for systems of linear differential equations
• Differential relations of theta functions
• On the algebraic non-integrability of the Halphen system
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