In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of ...

We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All ...

We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All ...