Bi-normal trajectories in the Circular Restricted Three-Body Problem

Abstract

In this note, we show there exist infinitely many trajectories which are bi-normal (i.e. normal at initial and final times) to the xz-plane, in the Spatial Circular Restricted Three-Body Problem, for energies below or slightly above the first critical value and near the primaries, under the assumption of the twist condition as defined by Moreno-van-Koert in arXiv:2011.06562. This is an application of the relative Poincar\'e-Birkhoff theorem for Lagrangians in Liouville domains, as proven by the authors in arXiv:2408.06919.