Branches of Orbits and Symbolic Dynamics for the Restricted Planar 3-body Problem

Gianni Arioli, Department of Mathematics, Politecnico di Milano, Italy

We consider the restricted planar 3-body problem. By applying topological methods and the implicit function theorem we give a computer-assisted proof of the existence and the linear stability or instability of continuous branches of periodic orbits, with the energy or the masses of the primaries as parameters. We provide an approximation of the orbits with rigorous bounds. We prove the existence of symbolic dynamics and we give a rigorous lower estimate for the topological entropy of the system.