Investigating the relation between chaos and the three body problem

TL;DR

This paper reviews the properties of fractals and chaos, focusing on three-body systems, classifying their behaviors, and emphasizing the importance of ongoing reviews due to the infinite solutions and potential applications.

Contribution

It provides a comprehensive review and classification of three-body systems related to chaos theory, highlighting the need for regular updates and exploring diverse solutions.

Findings

Three classes of three-body systems identified based on their properties

Infinite solutions exist for three-body systems, with potential applications beyond hierarchical systems

Regular reviews are recommended to keep track of evolving solutions

Abstract

We review the properties of fractals, the Mandelbrot set and how deterministic chaos ties to the picture. A detailed study on three body systems, one of the major applications of chaos theory was undertaken. Systems belonging to different families produced till date were studied and their properties were analysed. We then segregated them into three classes according to their properties. We suggest that such reviews be carried out in regular intervals of time as there are an infinite number of solutions for three body systems and some of them may prove to be useful in various domains apart from hierarchical systems.