Retratos de fase de uma família de sistemas cúbicos planares integráveis com duas parábolas invariantes

Abstract

In this work we present results of the qualitative theory of Ordinary Differential Equations used in the study of planar vector fields. Then, we apply these results to determine the global phase portrait in the Poincaré disk, of a family of planar cubic integrable vector fields with two invariant parabolas. As far as we know, this family has not yet been studied.