Symplectic completion of symplectic jets

In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in general) has an infinite Taylor series. In practice, we can compute only a finite number of terms in this series. This gives rise to a truncated map approximation of the original map. This truncated map is however not symplectic and can lead to wrong stability results when iterated. In this paper, following a generalization of the approach pioneered by Irwin (SSC Report No. 228, 1989), we factorize the map as a product of special maps called open-quote open-quote jolt maps close-quote close-quote in such a manner that symplecticity is maintained. copyright 1996 American Institute of Physics