# Are L1 to L2 and back “cheap” transfers/cyclers possible?

This paper studies transfers from halo orbit to halo orbit in the Jovian system. I wonder if there are any locally stable orbits connecting Earth-Moon L1 and L2 points.

EDIT: One should also consider trajectories based on low-thrust engines (ion, solar sails, magsails).

For a specific example, consider the Genesis mission design, which employs manifold transfers between periodic orbits. Technically, there is some math that says it takes infinite time to arrive from the manifold, so if we could wait an infinite time, it would be "free"--but we don't have time for that, so maneuvers will solve that issue. Here's a paper from CalTech that looks at heteroclinic connections between perioidic orbits--but not specifically in the Earth-Moon system (but, as an aside, the great thing about the system dynamics in the circular-restricted three body problem, the only real free parameter is the system mass ratio, usually $\mu$, that you can easily change to represent the system)