The vanishing twist in the restricted three-body problem

This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Near the Lagrangian equilibrium L 4 a twistless torus is created near the tripling bifurcation of the short period family. Decreasing the mass ratio leads to twistless bifurcations which are particularly prominent for rotation numbers 3 / 10 and 2 / 7 . This scenario is studied by numerically integrating the regularised Hamiltonian flow, and finding rotation numbers of invariant curves in a two-dimensional Poincaré map. roborate the numerical results the Birkhoff normal form at L 4 is calculated to eighth order. Truncating at this order gives an integrable system, and the rotation numbers obtained from the Birkhoff normal form agree well with the numerical results. A global overview for the mass ratio μ ∈ ( μ 4 , μ 3 ) is presented by showing lines of constant energy and constant rotation number in action space.