Integrable polynomial factorization for symplectic systems

It has been shown that an analytic symplectic map can be directly converted into a product of Lie transformations in the form of integrable polynomial factorization with the desired accuracy. A map in the form of integrable polynomial factorization is exactly symplectic and easy to evaluate exactly. Error involved in the integrable polynomial factorization has been studied with the case of the Henon map. The results suggest that the map in the form of integrable polynomial factorization is a reliable and convenient model for the study of the long-term behavior of a symplectic system such as a large storage ring