A class of periodic solutions of the N-body problem

We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in ^m (any m 2) where one of the bodies has mass equal to 1 and the others have masses ₂,...,_N, small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass _i moves close to one of the circular solutions of the two body problem of period T/k_i, where ki is any odd number. No relation has to be satisfied by k₂,...,k_N.