Integrable polynomial factorization for symplectic systems

Symplectic maps for approximating polynomial Hamiltonian systems

We study how to approximate polynomial Hamiltonian systems by composition of symplectic maps. Recently, a number of methods preserving the symplectic character have appeared. However, they are not completely satisfactory because, in general, they are computationally expensive, very difficult to obtain or their accuracy is relatively low. The efficiency of a numerical method depends on both its computational cost and its accuracy. Polynomial Hamiltonians are separable in exactly solvable parts, and this can be done in many different ways. Here we study how to find a separation for the Hamiltonian in a small number of cheaply computed terms. Since the proposed methods depend on some free parameters, we also indicate how to choose these parameters in order to improve the accuracy without increasing the computational cost.