  Long-term stability studies of nonlinear Hamiltonian systems require
symplectic integration algorithms which are both fast and accurate. In this
paper, we study a symplectic integration method wherein the symplectic map
representing the Hamiltonian system is refactorized using polynomial symplectic
maps. This method is analyzed in detail for the three degree of freedom case.
We obtain explicit formulas for the action of the constituent polynomial maps
on phase space variables.
