The vanishing twist in the restricted three-body problem

作者：Dullin Holger R; Worthington Joachim^*

来源：Physica D: Nonlinear Phenomena , 2014, 276: 12-20.

DOI：10.1016/j.physd.2014.03.001

• Vanishing twist
• Reconnection bifurcation
• Circular restricted three-body problem
• Poincare's surface of section
• Normal forms

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 Poincare map.
To corroborate 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 mu is an element of (mu(4), mu(3)) is presented by showing lines of constant energy and constant rotation number in action space.

• 出版日期2014-5-15