Galoisian obstructions to non-Hamiltonian integrability

We show that the main theorem of Morales, Ramis and Simo (2007) [6] about Galoisian obstructions to meromorphic integrability of Hamiltonian systems can be naturally extended to the non-Hamiltonian case. Namely, if a dynamical system is meromorphically integrable in the non-Hamiltonian sense, then the differential Galois groups of the variational equations (of any order) along its solutions must be virtually Abelian. (C) 2010 Published by Elsevier Masson SAS on behalf of Academie des sciences.