Numerical computations of normal forms around some periodic orbits of the restricted three-body problem

Diagonal Barcelona Spain Email jorditereupces In this paper we introduce a general methodology for computing numerically the normal form around a periodic orbit of an autonomous analytic Hamiltonian system The process follows two steps First we expand the Hamiltonian in suit able coordinates around the orbit and second we perform a standard normal form scheme based on the Lie series method This scheme is carried out up to some nite order and neglecting the remainder we obtain an accurate description of the dynamics in a small enough neighbourhood of the orbit In particular we obtain the invariant tori that generalize the elliptic directions of the periodic orbit On the other hand bounding the remainder one obtains lower estimates for the diusion time around the orbit This procedure is applied to an elliptic periodic orbit of the spatial Restricted Three Body Problem The selected orbit belongs to the Lyapunov family associate