An extensive search for stable periodic orbits of the equal-mass zero angular momentum three-body problem

TL;DR

This paper explores the stability regions of the equal-mass zero angular momentum three-body problem, identifying numerous new stable periodic orbits and analyzing their potential KAM stability through detailed initial condition analysis.

Contribution

It provides a comprehensive analysis of stability regions and discovers many new periodic orbits, characterizing their syzygy patterns and stability properties.

Findings

Four stability regions identified

971 stable periodic collisionless orbits verified

Many new orbits potentially KAM-stable

Abstract

A special 2D initial conditions' domain of the equal-mass zero angular momentum planar three-body problem, which has been formerly studied, is analyzed to deepen the knowledge of the stability regions in it. The decay times in the domain are carefully computed. Four stability regions are established. 971 verified initial conditions for linearly stable periodic collisionless orbits are found. Many of these identified initial conditions are new ones. The periodic orbits of each stability region are characterized by a certain pattern in their syzygy sequences. Additional computations show that the orbits found should be considered as candidates for KAM-stable orbits.