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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Ferragut, A.¹  Galindo, C.^2,3  Monserrat, F.⁴ 

[1] Univ Int Rioja, Ave Paz 137, Logrono 26006, Spain

[2] Univ Jaume 1, Inst Univ Matemat & Aplicac Castellon IMAC, Castellon de La Plana 12071, Spain

[3] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

[4] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, E-46022 Valencia, Spain

关键词: Planar polynomial vector field;    Darboux first integral;    Reduction of singularities;    Curve with only one place at infinity;   

DOI  :  10.1016/j.jmaa.2019.05.052

来源: Elsevier

【 摘 要 】

We study the class of planar polynomial vector fields admitting Darboux first integrals of the type Pi(r)(i=1) f(i)(alpha i), where the alpha(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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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