Saddle connections in a rotated vector field.

In this paper, we study the connections between two saddles in a rotated vector field, where one saddle lies in R2 and the other is located at infinity. We provide sufficient conditions for the existence of a heteroclinic connection and also of infinitely many heteroclinic connections between two saddles, one in the finite plane and another at infinity. These results are applied to a degenerate Bogdanov-Takens system with symmetry and to a cubic Liénard system, yielding complete global phase portraits on the Poincaré disk.