Computation of the invariant manifolds of infinity in the restricted circular planar three body problem with the parametrization method

Abstract

This work analyses the parabolic stable manifolds of the periodic orbits at infinity for the Restricted Planar Circular Three Body Problem. Using the parametrization method we prove the existence of such manifold and we compute an approximate parametrization K with an internal dynamic Y. That leads to numerical computations that will be analysed and compared with a similar methodology called the graph transform method.