Computation of homological equations for Hamiltonian normal form

Abstract

The procedure of deriving homological equations of arbitrary order, which solutions are used in iterative procedure of normalization of a Hamiltonian in a neighborhood of an equilibrium position, is considered. A formula for a homological equation of arbitrary order used in the method of normalization by means of the Lie series is proposed. The normalization procedure is applied to 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.