Normal form of a Hamiltonian system with a periodic perturbation

A perturbed Hamiltonian system with a time-independent unperturbed part and a time-periodic perturbation is considered near a stationary solution. First, the normal form of an autonomous Hamiltonian function is recalled. Then the normal form of a periodic perturbation is described. This form can always be reduced to an autonomous Hamiltonian function, which makes it possible to compute local families of periodic solutions of the original system. First approximations of some of these families are found by computing the Newton polyhedron of the reduced normal form of the Hamiltonian function. Computer algebra problems arising in these computations are briefly discussed.