Bifurcation near Boundaries of Regions of Stability of Libration Points in the Three-Body Problem

Abstract

The construction of regions of stability in a linear approximation for the triangular libration points in the planar, elliptical, restricted three-body problem is considered, together with the main scenarios for bifurcation when the parameters of the system pass through a boundary of such a region. A new scheme for constructing the boundaries of regions of stability is proposed, which leads to approximate formulas describing these boundaries. The resonance properties of the boundary points (from the point of view of the theory of local bifurcations) are studied. It is shown that one of the main scenarios for bifurcation is the appearance of non-stationary, 4π-periodic solutions close to a triangular libration point.