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arXiv · 1808.03512

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

A. Ferragut·C. Galindo·F. Monserrat
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Abstract

We study the class of planar polynomial vector fields admitting Darboux first integrals of the type $\prod_{i=1}^r f_i^{\alpha_i}$, 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.

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A. Ferragut, C. Galindo, F. Monserrat. 2018-08-10. On the computation of Darboux first integrals of a class of planar polynomial vector fields. https://arxiv.org/abs/1808.03512

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