Polynomial first integrals of quadratic vector fields

DOI10.1016/j.jde.2006.07.022zbMath1117.34035OpenAlexW1992378476MaRDI QIDQ860740

José Angel Rodríguez, Javier Chavarriga, Jaume Llibre, Belén García, Jesús S. Pérez del Río

Publication date: 9 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.07.022

zbMATH Keywords

polynomial first integralquadratic differential equation

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) Explicit solutions, first integrals of ordinary differential equations (34A05) Dynamics induced by flows and semiflows (37C10)

Related Items (14)

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ A survey on the inverse integrating factor ⋮ Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\) ⋮ On the polynomial differential systems having polynomial first integrals ⋮ Exactly solvable quadratic differential equation systems through generalized inversion ⋮ Quadratic system with a rational first integral of degree 2: a complete classification in the coefficient space \(\mathbb{R}^{12}\) ⋮ Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems ⋮ Polynomial inverse integrating factors for quadratic differential systems ⋮ Phase portaits of the quadratic vector fields with a polynominal first integral ⋮ Analytic integrability of quadratic–linear polynomial differential systems ⋮ Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3 ⋮ THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE ⋮ Quadratic systems with a polynomial first integral: A complete classification in the coefficient space \(\mathbb R^{12}\) ⋮ PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE INTEGRATING FACTOR

Cites Work

• Chordal quadratic systems
• Equations de Pfaff algébriques
• On the integrability of two-dimensional flows
• Polynomial first integrals of the Lotka-Volterra system
• Polynomial first integrals of quadratic systems.
• Liouvillian first integrals for the planar Lotka-Volterra system
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Invariant algebraic curves and conditions for a centre
• Integrability of the 2D Lotka-Volterra system via polynomial first integrals and polynomial inverse integrating factors
• On the polynomial first integrals of the (a,b,c) Lotka–Volterra system
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