Instability of three-body periodic collisionless equal-mass free-fall orbits

Abstract This work is a continuation of our recent work Celest Mech Dyn Astron 136, 7, (2024) . Here we give more details about the high-precision numerical methods used and present the results for the linear stability investigation of the found periodic orbits. The eigenvalues of the monodromy matrices for all periodic orbits are computed with high-precision and given with 30 correct digits. All found periodic orbits are unstable, more precisely they are of a hyperbolic-hyperbolic or a hyperbolic-elliptic type. This result gives rise to a hypothesis that the three-body periodic collisionless equal-mass free-fall orbits are unstable ones. The additionally made high-precision computations for the escape-times in the two dimensional initial conditions’ domain also support this hypothesis. A discussion in relation to chaos theory is held.