Integrability of centers perturbed by quasi-homogeneous polynomials

The objective of this work is to give sufficient and necessary conditions for integrability of differential equation systems in the plane of the form (x) over dot = -y(2p-1) + X-2(x, y), (y) over dot = x(2q-1) + Y-2(x, y), where X-2(x, y) and Y-2(x, y) are (p - q) quasi-homogeneous polynomials of degree 2 pq - q + 1 and 2 pq - p + 1, respectively. (C) 1997 Academic Press.