DARBOUXIAN INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS WITH SPECIAL EMPHASIS ON THE TWO-DIMENSIONAL SURFACES

DOI10.1142/S0218127402006187zbMath1047.34026MaRDI QIDQ4736323

Jaume Llibre, Gerardo Rodriguez

Publication date: 9 August 2004

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

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (4)

On the number of invariant conics for the polynomial vector fields defined on quadrics ⋮ Darboux integrability and reversible quadratic vector fields ⋮ A survey on the Kovalevskaya exponents and their applications ⋮ Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Cites Work

• On the complete and partial integrability of non-Hamiltonian systems
• Equations de Pfaff algébriques
• The limit cycle of the van der Pol equation is not algebraic
• Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires
• Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces
• Area preserving flows on compact connected surfaces
• Sur ĽintÉgration algÉbrique des Équations diffÉrentielles du premier ordre et du premier degrÉ
• Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
• Invariant algebraic curves and conditions for a centre
• Integrals of nonlinear equations of evolution and solitary waves
• Uniqueness of algebraic limit cycles for quadratic systems

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