Some remarks about the integration of polynomial planar vector fields.

DOI10.1007/BF02969331zbMath1054.34003MaRDI QIDQ1415964

Jean Moulin Ollagnier

Publication date: 9 December 2003

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

Darboux integrabilityplanar polynomial vector fields

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (3)

Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system ⋮ Liouvillian first integrals for the planar Lotka-Volterra system ⋮ Équations d'amorçage d'intégrales premières formelles

Cites Work

• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• Equations de Pfaff algébriques
• Polynomial first integrals of the Lotka-Volterra system
• Liouvillian integration of the Lotka-Volterra system
• Rational integration of the Lotka-Volterra system
• On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development
• Integrability and alegbraic solutions for the 2-D lotka-Volterra system
• Liouvillian First Integrals of Differential Equations
• On a Result of Darboux
• Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields
• Around Jouanolou non-integrability theorem
• About a conjecture on quadratic vector fields

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