Darboux theory of integrability for a class of nonautonomous vector fields

DOI10.1063/1.3205450zbMath1283.34027OpenAlexW2084808738MaRDI QIDQ3583619

Jaume Llibre, Chara Pantazi

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/7539

zbMATH Keywords

bifurcationlinear differential equationspolynomialspartial differential equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamics induced by flows and semiflows (37C10)

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Liouvillian integrability of polynomial differential systems, Liouvillian integrability versus Darboux polynomials, Oscillations on one dimensional time dependent center manifolds: algebraic curves approach, Integrability and solvability of polynomial Liénard differential systems, Non-autonomous inverse Jacobi multipliers and periodic orbits of planar vector fields, Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane, On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory, Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems

Cites Work

• Unnamed Item
• On the global flow of a 3-dimensional Lotka-Volterra system
• A family of isochronous foci with Darboux first integral
• Multiplicity of invariant algebraic curves in polynomial vector fields
• On the complete and partial integrability of non-Hamiltonian systems
• Configurations of limit cycles and planar polynomial vector fields.
• Generalized cofactors and nonlinear superposition principles
• Mass inflation and chaotic behaviour inside hairy black holes
• Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity
• On the integrability of the Einstein-Yang-Mills equations
• Inverse Jacobi multipliers
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Integrability of the Bianchi IX system
• Generalizations of Noether’s Theorem in Classical Mechanics
• Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
• DARBOUX INTEGRABILITY FOR THE RÖSSLER SYSTEM
• Invariant algebraic surfaces of the Lorenz system
• Integrals of nonlinear equations of evolution and solitary waves