The motions asymptotic to libration points

The plane restricted circular three-body problem is considered. The question of the existence of the trajectories which are asymptotic to the libration points is solved completely in the case when the libration points are exponentially unstable in linear approach. The method of construction of these asymptotic trajectories in the form of series is presented. Actually the construction of such series with accuracy within five members in respect to auxiliary variables is performed on computer using Deprit-Hori normalization method of Hamiltonian systems. The results of calculations are presented.