On the polynomial integrability of the Hoyer systems

Abstract

Agraïments: The second author is supported by FCT through the project PTDC/MAT/117106/2010 and through CAMGSD, Lisbon.

The Hoyer polynomial differential systems depend on nine parameters. We provide necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how can be computed the polynomial first integrals of these systems using the Kovalevsky exponents.