Bi-normal trajectories in the circular restricted three-body problem

Abstract In this note, we study existence of infinitely many trajectories bi-normal (i.e. normal at initial and final times) to the xz -plane in the Spatial Circular Restricted Three-Body problem, in the convexity range and near the primaries, under the assumption of the twist condition as defined by Moreno–van-Koert in [10]. Modulo our assumptions, this is an expected application of the relative Poincaré–Birkhoff theorem for Lagrangians in Liouville domains, as proven by the authors in [8].