Obstructions to the continuation of analytic integrals of Hamiltonian systems under non-Hamiltonian perturbations

In this Letter we consider n degrees-of-freedom integrable Hamiltonian syst ems subjected to a non-Hamiltonian perturbation controlled by a small param eter epsilon. An obstruction to the analytic continuation of the integrals of motion of the unperturbed system with respect to epsilon is developed fo r sufficiently small perturbations. The theory is applied to a perturbed sy stem of Morse oscillators. (C) 2001 Published by Elsevier Science B.V.