Homological equation of arbitrary order and computation of the normal form of a Hamiltonian system

In the preprint the procedure of deriving homological equations of arbitrary order, the solutions of which are used for the iterative procedure of normalization of the Hamiltonian in the neighborhood of the equilibrium position, is considered. The features of the implementation of the normalization algorithm using modern computer algebra systems are discussed. The normalization procedure is applied to the Hamiltonian of the Hill problem written in scaled regular variables. The resulting normal form of the Hill problem can be used to find sets of analyticity of the normalizing transformation.