Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem

In this paper, we construct stability regions (in the linear approximation) of triangular libration points for the planar, bounded, elliptical three-body problem and examine bifurcations that occur when parameters of the system pass through the boundaries of these regions. A new scheme for the construction of stability regions is presented, which leads to approximation formulas describing these boundaries. We prove that on one part of the boundary, the main scenario of bifurcation is the appearance of nonstationary $4\pi$-periodic solutions that are close to a triangular libration point, whereas on the other part, the main scenario is the appearance of quasiperiodic solutions.