Galoisian obstruction to the integrability of general dynamical systems (Q414822)

Recently, \textit{M. Ayoul} and \textit{Nguyen Tien Zung} [C. R., Math., Acad. Sci. Paris 348, No. 23--24, 1323--1326 (2010; Zbl 1210.37076)] obtained a necessary condition of integrability for non-Hamiltonian systems. They showed that if the given complex dynamical system is integrable, then the differential Galois group of the variational equations along a non-stationary solution is commutative. In this paper the authors analyze the integrability of general dynamical systems by Galoisian approach. They obtain some necessary conditions of the system to possess a certain number of integrals. Several applications are given at last to illustrate this results.