A constructive algorithm for the normalization of a periodic hamiltonian

A time-periodic Hamiltonian system is considered. It is assumed that the system has an equilibrium position in whose neighbourhood the Hamiltonian is analytic. A constructive algorithm is proposed for computing the coefficients of the normal form of the Hamiltonian. The algorithm is based on a special procedure for the construction and analysis of a symplectic map of the neighbourhood of the equilibrium position onto itself. The exposition is carried out using as an example a system with two degrees of freedom. The coefficients of the normal form are expressed in terms of the coefficients of the generating function of the map. The algorithm is used to solve the problem of the stability of the relative equilibrium of a Kovalevskaya top with a vertically oscillating suspension point.