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 H amiltonian system as a symplectic map. This map (in general) has an in finite Taylor series. In practice, we can compute only a finite number of terms in this series. This gives rise to a truncated map approxima tion 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 Re port No. 228, 1989), we factorize the map as a product of special maps called ''jolt maps'' in such a manner that symplecticity is maintaine d. (C) 1996 American Institute of Physics.