Kozai resonance in coorbital planets

In hierarchical systems, the secular resonance Lidov-Kozai (LK) provides conditions for periodic orbits for inclined systems. When we study a system within the coorbital resonance (almost equal mean motions between the secondary bodies) there is some controversy about the existence of such periodic orbits. Using an N-body integrator, we have found that the phase space of the general three-body problem is different to the restricted case for an inclined system, and we establish the location of the Lidov-Kozai equilibrium configurations depending on the mass ratio.