Darboux integrability and invariant algebraic curves for planar polynomial systems

DOI10.1088/0305-4470/35/10/310zbMath1012.34035OpenAlexW2123143010MaRDI QIDQ4545233

Chara Pantazi, Xiang Zhang, Jaume Llibre, Colin Christopher

Publication date: 15 August 2002

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

Full work available at URL: http://hdl.handle.net/2117/1205

zbMATH Keywords

Darboux integrabilityplanar polynomial systemsinvariant algebraic curves

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14)

Related Items (24)

Darboux integrability of the simple chaotic flow with a line equilibria differential system ⋮ Planar quadratic vector fields with invariant lines of total multiplicity at least five ⋮ On the 16th Hilbert problem for algebraic limit cycles ⋮ Inverse problems in Darboux' theory of integrability ⋮ Limit cycles in Kukles systems of arbitrary degree with invariant ellipse ⋮ Darboux integrating factors: inverse problems ⋮ On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves ⋮ Characterization of the Kukles polynomial differential systems having an invariant algebraic curve ⋮ On the centers of cubic polynomial differential systems with four invariant straight lines ⋮ Unnamed Item ⋮ Planar vector fields with a given set of orbits ⋮ On the limit cycles bifurcating from an ellipse of a quadratic center ⋮ Calculation of singular point quantities at infinity for a type of polynomial differential systems ⋮ On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Darboux invariants for planar polynomial differential systems having an invariant conic ⋮ Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems ⋮ Polynomial differential systems having a given Darbouxian first integral ⋮ Rational general solutions of planar rational systems of autonomous ODEs ⋮ Invariant curves and integrability of planar \(\mathcal C^r\) differential systems ⋮ Attracting and natural invariant varieties for polynomial vector fields and control systems ⋮ Unnamed Item ⋮ Some remarks on global analytic planar vector fields possessing an invariant analytic set ⋮ Polynomial Vector Fields on the Clifford Torus

This page was built for publication: Darboux integrability and invariant algebraic curves for planar polynomial systems