Planar quasi-homogeneous polynomial differential systems and their integrability.

Abstract: In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3. The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. [Copyright &y& Elsevier]