Bifurcation at nonsemisimple 1:-1 resonance (Q1085638)

The restricted three body problem describes the movement of a massless body P subject to the attracting forces of two primary bodies of masses 1 - \(\mu\) and \(\mu\) rotating in circles about their common centre of mass. This paper is concerned with the motion of P in the neighbourhood of the equilateral equilibria of the system. A bifurcation occurs when the mass parameter \(\mu\) passes through the critical value of Routh. The system is Hamiltonian with two degrees of freedom and it is shown that the bifurcation is an example of nonsemisimple 1:-1 resonance.