Normalization of the non-autonomic linear Hamiltonian system with a small parameter

An algorithm for constructing the normalizing transformation for the linear Hamiltonian system of differential equations with periodic coefficients is proposed where the matrix of transformation is represented in the form of power series in a small parameter. The recurrence relations for coefficients of the corresponding series are obtained and the matrices of transformation for the second and the fourth order systems arising in the study of the stability of equilibrium solutions in restricted elliptic many-body problems are calculated.