POLYNOMIAL INVERSE INTEGRATING FACTORS

Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important role in the problem of the center and in the determination of limit cycles. In this paper we obtain necessary conditions for a polynomial vector field (P, Q) to have a polynomial inverse integrating factor.