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

    Autor: 
    Ferragut, Antoni (1)
    Galindo, Carlos
    Monserrat, Francisco
    Fecha: 
    15/10/2019
    Palabra clave: 
    planar polynomial vector field; darboux first integral; reduction of singularities; curve with only one place at infinity; Scopus; JCR
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/9354
    DOI: 
    https://doi.org/10.1016/j.jmaa.2019.05.052
    Dirección web: 
    https://www.sciencedirect.com/science/article/abs/pii/S0022247X19304603?via%3Dihub
    Open Access
    Resumen:
    We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏i=1 rfi αi, where the αi's are positive real numbers and the fi'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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