We consider the planar circular Hill’s problem and its limiting case called the intermediate H´enon problem. The Hill’s problem is a singular perturbation of the former. There is a countable set of generating arc–solutions each of them is defined by the condition of passing through the singular point of the Hill’s problem. It is shown that each arc–solution has its own invariant manifold defined by the additional first integral of motion of the intermediate H´enon problem. The generating solutions of families of periodic orbits of the Hill’s problem are built from the arc-solutions like words are composed from letters. The set of all the right composed “words” defines the symbolic dynamics of the system.

Mathematical problems and theory of numerical methods