Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

DOI10.1007/BF02871455zbMath1194.34050MaRDI QIDQ2569758

Jaume Llibre, Xiang Zhang

Publication date: 20 October 2005

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

zbMATH Keywords

spheretorusDarboux integrabilitygeneralized cylinder

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34)

Related Items (14)

On the integrability of the Einstein-Yang-Mills equations ⋮ On the non-integrability of a generalized Darboux Halphen system ⋮ Darboux theory of integrability for polynomial vector fields on 𝕊ⁿ ⋮ Limit cycles for planar piecewise linear differential systems via first integrals. ⋮ Seeking Darboux polynomials ⋮ RATIONAL FIRST INTEGRALS FOR POLYNOMIAL VECTOR FIELDS ON ALGEBRAIC HYPERSURFACES OF ℝⁿ⁺¹ ⋮ Darboux integrability and algebraic limit cycles for a class of polynomial differential systems ⋮ The Michelson system is neither global analytic, nor Darboux integrable ⋮ Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\) ⋮ Invariant circles for homogeneous polynomial vector fields on the 2-dimensional sphere ⋮ Planar polynomial vector fields having first integrals and algebraic limit cycles ⋮ DARBOUXIAN INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS WITH SPECIAL EMPHASIS ON THE TWO-DIMENSIONAL SURFACES ⋮ Liouvillian first integrals for the planar Lotka-Volterra system ⋮ Integrability of the Bianchi IX system

Cites Work

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• Equations de Pfaff algébriques
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• Polynomial first integrals of the Lotka-Volterra system
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• Invariant hyperplanes and Darboux integrability for \(d\)-dimensional polynomial differential systems
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Invariant algebraic curves and conditions for a centre
• Darbouxian first integrals and invariants for real quadratic systems having an invariant conic
• Darboux integrability for 3D Lotka-Volterra systems
• DARBOUXIAN INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS WITH SPECIAL EMPHASIS ON THE TWO-DIMENSIONAL SURFACES

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