Application of Gauss's method in the formation of periodic solutions in the relativistic restricted problem of three bodies

The paper discusses the existence of periodic and quasi-periodic solutions in the space relativistic problem of three bodies with the help of Poincaré's small parameter method starting from non-Keplerian generating solutions, i.e., using Gauss's method. The main peculiarity of these periodic orbits is the fact that they close, in general, after many revolutions. It is worth noticing that these periodic orbits give a new class of periodic solutions of the classical circular problem of three bodies, if relativistic effects are neglected.