On the computation of Darboux first integrals of a class of planar polynomial vector fields

2018/08/10 by Antoni Ferragut, Ferragut, A., Carlos Galindo +3
Mathematics · #14C21 #34A34 #34C05 #34C08 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1808.03512

openalex publication_date 2018/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏_i=1^r f_i^α_i, where the α_i's are positive real numbers and the f_i's are polynomials defining curves with only one place at infinity. We show that these vector fields have an extended reduction procedure and give an algorithm which, from a part of the extended reduction of the vector field, computes a Darboux first integral for generic exponents.

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