A classical trajectory study of Ar + Ar-2 collisions is described. The system provides a model chaotic scattering system in more than two degrees of freedom. The initial conditions that give rise to ejection of each of the three Ar atoms, and the corresponding collision mechanisms, are investigated. There are some large regions of the initial condition space in which the identity of the atom ejected does not change, and other regions in which it changes rapidly. Attention is focused on long-lived trajectories, which lie at the boundaries between different product identities. The long-lived trajectories are associated with sequences of periodic orbits. The different stability possibilities for periodic orbits in three degrees of freedom are discussed, and a sequence of periodic orbits responsible for dividing the initial condition space is identified. These periodic orbits are born at "avoided bifurcations," at which a saddle-center bifurcation occurs close to a parent periodic orbit. The generalization to systems with more than three degrees of freedom is discussed.