Global phase portraits of some reversible cubic centers with collinear or infinitely many singularities

Abstract

Agraïments: Furthermore the first author also is supported by the Juan de la Cierva grant number JCI-2007-49-764 and the second author also is partially supported by ICREA Academia.We study the reversible cubic vector fields of the form ˙x = −y + ax2 + bxy + cy2 − y(x2 + y2), y˙ = x + dx2 + exy + fy2 + x(x2 + y2), having simultaneously a center at infinity and at the origin. In this paper the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological and diffeomorphic equivalence