RATIONAL FIRST INTEGRALS FOR POLYNOMIAL VECTOR FIELDS ON ALGEBRAIC HYPERSURFACES OF ℝn+1

DOI10.1142/S0218127412502707zbMath1258.34007MaRDI QIDQ4908375

Jaume Llibre, Yudy Bolaños

Publication date: 5 March 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

polynomial vector fieldsDarboux theory of integrabilityalgebraic hypersurfacesrational first integrals

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Ordinary differential equations and systems on manifolds (34C40)

Related Items (4)

Darboux theory of integrability for polynomial vector fields on 𝕊ⁿ ⋮ Invariant hyperplane sections of vector fields on the product of spheres ⋮ Invariant circles and phase portraits of cubic vector fields on the sphere ⋮ Normal forms of polynomial differential systems in \(\mathbb{R}^3\) having at least three invariant algebraic surfaces

Cites Work

• Curvature on the Fermat cubic
• Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires
• Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\)
• Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces
• Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
• HILBERT'S MODULAR GROUP OF THE FIELD $ \mathbf Q(\sqrt 5)$ AND THE CUBIC DIAGONAL SURFACE OF CLEBSCH AND KLEIN
• Integrals of nonlinear equations of evolution and solitary waves

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