The one-dimensional three-body problem: Numerical simulations

Abstract

The ergodic properties of a one-dimensional gravitational system belonging to the microcanonical ensemble are studied. This system, constituted of equal-mass particles, exhibits very strong binary structures which prevent the system to be ergodic and then to reach the theoretical curves predicted by Rybicki. The presence of the binary structure (called molecule is examined through two criterions. The first one is given by a topological property based on the order relation of the one-dimensional systems; the second one is the internal energy of the molecule. At last the study of the molecule stability indicates that it strongly depends on initial conditions.