Hamiltonian normal forms in the neighbourhoods of collinear libration points in the restricted circular three body problem

The fourth-degree Hamiltonian normal forms in the neighbourhoods of the collinear libration points in the restricted plane circular three-body problem are found using an invariant normalization algorithm. Exact relations between the coefficients of the normal forms and the ratio of the masses of the heavy bodies are obtained. The subspaces of the phase variables, the initial values of which determine the periodic trajectories in the neighbourhoods of the libration points, are found.