Different Types of attractors in the Three Body Problem perturbed by dissipative Terms

We study the evolution of a conservative dynamical system with three degrees of freedom, where small non conservative terms are added. The conservative part is a Hamiltonian system, describing the motion of a planetary system consisting of a star, with a large mass, and of two planets, with small but not negligible masses, that interact gravitationally. This is a special case of the three body problem, which is non integrable. We show that the evolution of the system follows the topology of the conservative part. This topology is critically determined by the families of periodic orbits and their stability. The evolution of the complete system follows the families of the conservative part and is finally trapped in the resonant orbits of the Hamiltonian system, in different types of attractors: Chaotic attractors, limit cycles or fixed points.