A new algorithm for finding rational first integrals of polynomial vector fields

DOI10.1007/s12346-010-0021-xzbMath1216.34001OpenAlexW2074539848MaRDI QIDQ611135

Antoni Ferragut, Hector J. Giacomini

Publication date: 14 December 2010

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/232172

zbMATH Keywords

planar polynomial vector fieldrational first integral

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) 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 (15)

Pegasus: sound continuous invariant generation ⋮ Invariant algebraic curves for Liénard dynamical systems revisited ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ Symbolic computations of first integrals for polynomial vector fields ⋮ Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time ⋮ Some new results on Darboux integrable differential systems ⋮ Detection of special curves via the double resultant ⋮ Local behavior of planar analytic vector fields via integrability ⋮ Liouvillian integrability of the generalized Duffing oscillators ⋮ Global \({C}^{\infty}\) integrability of cubic-linear polynomial differential systems ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ On the computation of Darboux first integrals of a class of planar polynomial vector fields

Uses Software

• Mathematica

Cites Work

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