A non-integrability test for perturbed separable planar Hamiltonians

We prove the non-integrability of perturbed separable planar potentials by using the perturbed normal variational equations, with a reasoning analogou s to Ziglin's theorem. We apply the above criterion to a Hamiltonian that c annot be proved non-integrable by other known non-integrability criteria. ( C) 2000 Elsevier Science B.V. All rights reserved.