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 ℝ m (any m ⩾ 2) where one of the bodies has mass equal to 1 and the others have masses εα2,...,∈α N , ε small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass εαi 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 k 2,...,k N