Fer's factorization as a symplectic integrator

In this paper we analyze the main features of the so-called Fer expansion as a new method for integrating the ordinary differential equations derived from explicitly time-dependent Hamiltonian dynamical systems, This method is based on a factorization of the evolution operator as an infinite product of exponentials of Lie operators and thus exactly preserves the Poincare integral invariants. Third and fourth-order expansions are considered and numerical results are presented for a quadratic Hamiltonian with various time-dependent frequencies. Comparison is done with other numerical integration schemes.