Universität Augsburg
Institut für Mathematik

Work in recent years has shown that, not only is the spatial circular restricted three-body problem a contact geometry problem for low energies, but also that it admits an open book decomposition whose pages are Liouville domains. We show the existence of a particular Lagrangian in these pages: the collision Lagrangian. Then, a Poincaré-Birkhoff type theorem gives the existence of infinitely many orbits of (consecutive) collision.

The proof of this theorem requires the introduction of local wrapped Floer homology, whose construction we shall discuss. Then, we will discuss other Lagrangians of interest in the spatial circular three-body problem; and what we could learn from them.