Symplectic integration of Hamiltonian systems using polynomial maps

In order to perform numerical studies of long-term stability in nonlinear H amiltonian systems, one needs a numerical integration algorithm which is sy mplectic. Further, this algorithm should be fast and accurate. In this Lett er, 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 o f particle storage rings in accelerators. (C) 2001 Elsevier Science B.V. Al l rights reserved.