Structure of the phase space near Lagrange's triangular equilibrium points

We have constructed a mapping for the planar circular restricted three-body problem and used it to study the structure and stability of the phase spac e near the Lagrangian triangular points of libration. It is found that when the mass ratio of the primaries mu < 0.02165, and excepting the value mu = 0.01441, the libration point is surrounded by invariant curves, hence is s table. This is in agreement with theoretical result and demonstrates the ef fectiveness of the mapping method.