arXiv subjects

A. Ferragut

Publications and source records attributed to A. Ferragut.

2 recordsLinked to original sources

arXiv2018

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

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

math.DS↗

arXiv2014

A class of polynomial planar vector fields with polynomial first integral

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 Poincaré 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.

math.CA↗