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

Alexander B. Batkhin

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arXiv · 1411.4933

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

Alexander B. Batkhin

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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.

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Alexander B. Batkhin. 2014-11-17. Henon's generating solutions and the structure of periodic orbits families of the restricted three-body problem. https://arxiv.org/abs/1411.4933

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