Qualitative study of the planar isosceles three-body problem

The planar three body problem obtained when the masses form an isosceles triangle every time is considered for the flow on a fixed level of negative energy. A topological representation of the energy manifold including the triple collision and infinity as boundaries of that manifold is obtained. The existence of orbits connecting the triple collision and the infinity gives homoclinic and heteroclinic orbits. Using these orbits and the homothetic solutions of the problem, orbits which pass near triple collision and near infinity by pairs of sequences are characterized. One of the sequences describes the regions visited by the orbit, the other refers to the behavior of the orbit between two consecutive passages by a suitable surface of section. This symbolic dynamics, which has a topological character, is given in an abstract form and is applied to the isosceles problem.