Three-body problem, the measure of oscillating types. A short review

The theoretical three body problem, with three given non infinitesimal point masses, has two types of oscillating motions. In the first type at least two mutual distances are unbounded, but their inferior limit is bounded: there are an infinite number of larger and larger ejections, but without escape. In the second type, it is the velocities that are unbounded: there are an infinite number of nearer and nearer quasi-collisions, without exact collisions.

The first type has only a theoretical interest: its measure in phase space is zero. But the second type has a positive measure in phase space and a physical interest: it governs most of the collisions of stars.