Henon's generating solutions and the structure of periodic orbits families of the restricted three-body problem

TL;DR

This paper surveys Michel Hénon's work on periodic solutions in the restricted three-body and Hill problems, comparing his results with Alexander Bruno's and proposing a generalization to describe orbit families as networks.

Contribution

It provides a comprehensive overview of Hénon's contributions and introduces a new generalization of the Hill problem for describing periodic orbit families.

Findings

Comparison of Hénon's and Bruno's results on periodic solutions

Survey of Hénon's work on Hill problem

Proposal of a generalized Hill problem with orbit networks

Abstract

We propose a survey of Michel H\'enon works devoted to studying periodic solutions of the well-known celestial mechanics problem -- restricted three-body problem. The description of the main results obtained by H\'enon is given in comparison with results of russian mathematician Alexander Bruno. Finaly, a survey of H\'enon's works on Hill problem is given as well, and, more over, the authors propose some generalization of Hill problem that makes possible to provide the description of its families of periodic orbits in the form of common network.