On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems ✩

In this paper we first give a necessary condition for general nonlinear systems to have rational first integrals. Then by using the so-called Kowalevsky exponents we present a criterion for nonexistence of rational first integrals for semiquasihomogeneous systems. © 2007 Elsevier Inc. All rights reserved