ON THE NUMBER OF ISOLATING INTEGRALS IN PERTURBED HAMILTONIAN-SYSTEMS WITH N-GREATER-THAN-OR-EQUAL-TO-3 DEGREES OF FREEDOM

We consider a perturbed Hamiltonian system with n greater-than-or-equal-to 3 degrees of freedom of the form H = H-0 + epsilonH-1 and show that the properties of the average value of the perturbing function H-1 along the periodic orbits of the unperturbed integrable part H-0 supply criteria for non-integrability which restrict the allowed total number of independent integrals of motion.