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

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. • A special case of the zero angular momentum three-body problem is considered. • 971 verified linearly stable collisionless equal-mass periodic orbits i.c.s are found. • High precision linear stability data (eigenvalues and frequencies) are presented. • All i.c.s satisfy the non-resonance condition for KAM-stability. • Verified decay times’ results in the initial conditions’ domain are shown.