Analysis of resonances in the three body problem using planar reduction

The planar (circular restricted) three body problem in resonance is a model system for formal reduction to one degree of freedom. It is investigated in the neighborhood of the Lagrangian equilateral triangular solution. The reduction can be handled by equivariant singularity theory with one or two distinguished parameters, yielding an integrable approximation of the Poincaré map. This makes a concise description possible of certain bifurcations, which can be checked by numerical simulations.