A class of polynomial planar vector fields with polynomial first integral

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

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

[1] Univ Jaime I, Inst Univ Matemat & Aplicac Castello IMAC, Castellon de La Plana 12071, Spain

[2] Univ Jaime I, Dept Matemat, Castellon de La Plana 12071, Spain

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

关键词: Planar polynomial vector field;    Polynomial first integral;    Reduction of singularities;    Blow-up;    Invariant algebraic curve;    Curve with only one place at infinity;   

DOI  :  10.1016/j.jmaa.2015.04.062

来源: Elsevier

【 摘 要 】

We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral. In addition, we solve the Poincare problem for the class of systems which admit a polynomial first integral as above in the sense that the degree of the minimal first integral can be computed from the reduction of singularities of the corresponding vector field. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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