A topological existence proof for the schubart orbits in the collinear three-body problem

A topological existence proof is presented for certain symmetrical periodic orbits of the collinear three-body problem with two equal masses, called Schubart orbits. The proof is based on the construction of a Wazewski set W in the phase space. The periodic orbits are found by a shooting argument in which symmetrical initial conditions entering W are followed under the flow until they exit W. Topological considerations show that the image of the symmetrical entrance states under this flow map must intersect an appropriate set of symmetrical exit states.