Polynomial map symplectic algorithm
  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. 
Govindan Rangarajan