Computational methodologies for quasi-periodic orbits and invariant manifold connections in non-autonomous problems

Semi-analytical and numerical techniques to systematically analyze and compute natural connections between quasi-periodic orbits associated to non-autonomous systems are considered. Focusing in the non-autonomous Sun-Earth+Moon coherent qbcp model, the center-unstable and center-stable invariant manifolds of Lyapunov quasiperiodic orbits are parameterized and a methodology to detect heteroclinic connections between manifolds is introduced. The methodology aims to decrease the number of degrees of freedom of the problem and to address the issue of searching good initial conditions inside the high dimensional state space. In this way, connections are found by searching approximate patch points on a Poincaré section and then they are refined to obtain smooth connections. The procedure is suitable for the implementation of a continuation method in the families.