The roles of L4 and L5 axial orbits in transport among co-orbital orbits

This paper identifies L-4 and L-5 axial orbits as possible transport gateways among several types of co-orbital orbits in the Sun-Jupiter spatial circular restricted three-body problem. Computation of finite time Lyapunov exponents reveals dynamical boundaries among coorbital orbits in the high-dimensional phase space. We find that the visualized separatrices stem from L-4 or L-5 axial orbits, which are unstable periodic orbits bifurcated from the halo-family around one of the Lagrange points L-1. Invariant manifolds emanating from L-4 and L-5 axial orbits indicate that these unstable periodic orbits separate fates of co-orbital orbits into quasi-satellite orbits and tadpole orbits, horseshoe orbits, or passing orbits depending on their values of the Jacobi constant. Possible applications of L-4 and L-5 axial orbits to space mission trajectories are discussed.