Juan Jose MORALES-RUIZ

Dep. Matematica Aplicada II
Universitat Politecnica de Catalunya
c/Pau Gargallo 5
E-08028, Barcelona
Espagne
morales@ma2.upc.es

Non-integrability of Hamiltonian systems by means of the variational equations.

Abstract : It is proved that a necessary condition for complete integrability (in Liouville sense and with several degrees of regularity of the firts integrals) is that the identity component of the Galois group of the variational equation (in the complex domain) must be abelian. We test the efficacy of these results on several classical systems: Homogeneous Potentials, Three Body Problem, Bianchi IX Cosmological Model, etc...