On the computation of the Lyapunov characteristic numbers of the planar restricted three-body problem

We used the power series solution to discuss the computation of the Lyapunov Characteristic Numbers of the regularised equations of the planar restricted three-body problem, and found it to be more effective than the usual numerical methods (RK78, linear multi-step). Our results show that the Sundman type of power series solution can be used in practice. We also found that in the limiting case where the infinitisimal body is indefinitely close to either of the finite bodies, all the LCNs should be zero.