NON INTEGRABILITY CRITERIA FOR HAMILTONIANS IN THE CASE OF LAME NORMAL VARIATIONAL EQUATIONS Juan J. Morales-Ruiz(1) and Carles Simo(2) (1) Dept. de Matematica Aplicada II, Universitat Politecnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain. morales@ma2.upc.es (2) Dept. de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain. carles@maia.ub.es Abstract We consider complex analytic classical Hamiltonian systems with two degrees of freedom and an invariant plane. Furthermore we assume that the normal variational equations are of Lame type. We describe the possible potentials giving rise to this kind of problems and non integrability criteria based on the differential Galois approach to the Ziglin theorem. Some examples are included. AMS Subject Classification: 58F05