Statistics of the Distribution of Families of Periodic Solutions to Hill’s Problem

All generating solutions of families of periodic orbits of the planar circular Hill problem of the second type can be described in terms of limiting arc solutions of the integrable Hénon problem. Each generating solution is a finite sequence composed, according to certain rules, of a countable set of arcs of two types connected at the origin by a hyperbolic conic. Each generating solution determines the symmetry type, the global orbit multiplicity, and other characteristics of the corresponding periodic solutions to the generated family. The symbolic dynamics on a finite subset of arc solutions, which is used to calculate the statistics of the distribution of generated families by symmetry types is studied. For this purpose, a class hierarchy is implemented using the Python ecosystem, and simulation for three sets of arcs is carried out performed.