Hyperbolic Orbits for Restricted Three-body Problems with Fixed Energy

TL;DR

This paper proves the existence of hyperbolic orbits in certain restricted three-body problems with fixed energy by using variational methods and limit processes on periodic solutions.

Contribution

It introduces a novel approach to establish hyperbolic orbits in restricted three-body problems through variational techniques and limit analysis.

Findings

Existence of hyperbolic orbits proven for specific three-body problems.

Use of variational methods to construct periodic solutions.

Limit process applied to obtain hyperbolic orbits.

Abstract

The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.