Abstract

In 1996 Furta [1] and Goriely [2] proved, independently, the existence of a link between the Kowalevskaya exponents of quasi--homogeneous polynomial differential systems and the degree of their polynomial first integrals. Here, we provide a new link.
[1] S. D. Furta, On non-integrability of general systems of differential equations, Z. Angew Math. Phys. 47 (1996), 112-131.
[2] A. Goriely, Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations, J. Math. Phys. 37 (1996), 1871-1893.