Periodic and chaotic trajectories of the second species for the n-centre problem

For the n-centre problem of one particle moving in the potential of attract ing centres of small mass fixed in an arbitrary smooth potential and magnet ic field, we prove the existence of periodic and chaotic trajectories shado wing sequences of collision orbits. In particular, we obtain large subshift s of solutions of this type for the circular restricted 3-body problem of c elestial mechanics. Poincare had conjectured existence of the periodic ones and given them the name 'second species solutions'.