Normal form of a Hamiltonian system with a periodic perturbation

Near a stationary solution we consider the Hamiltonian system with such perturbation, that the unperturbed Hamiltonian function is autonomous and the perturbation of the Hamiltonian function is periodic in time. First we remind the normal form of the autonomous Hamiltonian function. Second we describe the normal form of the periodic perturbation of the Hamiltonian function. It can always be reduced to the time independent Hamiltonian. It allows to compute the local families of periodic solutions to the initial system. The first approximations of some of these families are found by means of computation of the Newton polyhedron of the reduced normal form of Hamiltonian. We also discuss problems of the computer algebra arising in these computations.