1 Introduction The following Hamiltonian system is considered [ "*&+ §£(*,?) = 0 [ q(t + T) = q(t),\/ten where q{ € R*, £ 3, 1 i n, 4 = (g1}..., gn) and V : » x Fn(K£) — ft. Here Fn(3^) denotes the nt/l configuration space on ffi Fn{&) = {(91,.... On) € (#)" / ft ? q, if i*j}. Since the arguments used here are valid for any choice of m* 0. 1 i take rrti = 1, 1 i n and write (1.1) as j j + V.Vft.J-O V is given by t . i = i where for each i, j the function Vf, is T-periodic in t and satisfies 1 Received by the editor November 11, 1993. 1

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