Symplectic Integration of Hamiltonian Systems using Polynomial Maps

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose such a symplectic integration algorithm using polynomial map refactorization of the symplectic map representing the Hamiltonian system. This method should be particularly useful in long-term stability studies of particle storage rings in accelerators.