Restricted N+1-body problem: existence and stability of relative equilibria

We consider n bodies (with equal mass m) disposed at the vertices of a regular n-gon and rotating rigidly around an additional mass m(0) (at its center) with a constant angular velocity (relative equilibrium). In the present paper, we prove results on the existence and on the linear stability of equilibrium positions for a zero-mass particle submitted to the gravitational field generated by the previous system.