Global Phase Portraits Of Some Reversible Cubic Centers With Collinear Or Infinitely Many Singularities

We study the reversible cubic vector fields of the form (x)over dot = -y + ax(2) + bxy + cy(2) - y(x(2) + y(2)), (y)over dot = x + dx(2) + exy + fy(2) + x(x(2) + y(2)), 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 equivalence.