Some new results on Darboux integrable differential systems

We deal with complex planar differential systems having a Darboux first integral H . We present a definition of remarkable values and remarkable curves associated to H and characterize the existence of a polynomial inverse integrating factor for these systems. Furthermore, we study the relation between the characteristic polynomial F and the inverse integrating factors of the system and show the importance of the numerator of the exponential factor of H in the construction of F .