Desingularizations of the restricted three-body problem

We consider the planar circular restricted three-body problem for small values of the mass ratio $\mu$. Unperturbed problem (i.e. the two-body problem in the rotating frame) has singular perturbations, related with the body with mass $\mu$, near the body and near a family of stationary points. Here we select the first approximations of the system near these singularities and propose the changes of coordinates which transform the first approximations into unperturbed systems.