Inverse problems for multiple invariant curves

DOI10.1017/S0308210506000400zbMath1144.34003OpenAlexW2108637720MaRDI QIDQ5437040

Chara Pantazi, Sebastian Walcher, Jaume Llibre, Colin Christopher

Publication date: 18 January 2008

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210506000400

zbMATH Keywords

Darboux integrabilityinvariant algebraic curvesDarboux integrating factorsPlanar polynomial vector fields

Mathematics Subject Classification ID

Plane and space curves (14H50) Explicit solutions, first integrals of ordinary differential equations (34A05) Dynamics induced by flows and semiflows (37C10) Qualitative theory for ordinary differential equations (34C99) Inverse problems involving ordinary differential equations (34A55)

Related Items (12)

Darboux polynomials and global phase portraits for the \(D_{2}\) vector field ⋮ Inverse problems in Darboux' theory of integrability ⋮ Invariant ideals of local analytic and formal vector fields ⋮ Darboux integrating factors: inverse problems ⋮ On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves ⋮ Classical quasi-steady state reduction -- a mathematical characterization ⋮ Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor ⋮ 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 ⋮ Invariant curves and integrability of planar \(\mathcal C^r\) differential systems ⋮ On planar polynomial vector fields with elementary first integrals

This page was built for publication: Inverse problems for multiple invariant curves