Generic polynomial vector fields are not integrable.

DOI10.1016/S0019-3577(04)90005-5zbMath1056.34059OpenAlexW2147690024WikidataQ104404997 ScholiaQ104404997MaRDI QIDQ1890412

Jean Moulin Ollagnier, Andrzej Nowicki, Andrzej J. Maciejewski

Publication date: 3 January 2005

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0019-3577(04)90005-5

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Dynamics induced by flows and semiflows (37C10) Qualitative theory for ordinary differential equations (34C99) Commutative rings of differential operators and their modules (13N10)

Related Items (5)

Rational constants of monomial derivations ⋮ Correction to: Generic polynomial vector fields are not integrable ⋮ Derivations of polynomial algebras without Darboux polynomials ⋮ Monomial Derivations ⋮ Équations d'amorçage d'intégrales premières formelles

Cites Work

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• On algebraic sets invariant by one-dimensional foliations on \(\mathbb{C} P(3)\)
• M. N. Lagutinskij (1871-1915): A misunderstood mathematician
• Liouvillian integration of the Lotka-Volterra system
• On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development
• Multi-dimensional Jouanolou system
• Around Jouanolou non-integrability theorem

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