  Solutions to the collinear three-body problem which do not end in triple
collision pass through an infinite number of binary collisions. Given three
masses, we show that four geometric quantities generate a finite description of
itineraries of binary collisions. In the best circumstances, this description
is semi-conjugate to a Poincare map of the flow. For other cases these
quantities give upper and lower bounds on the itineraries which can occur. In
addition to describing the dynamics of the collinear three-body problem, the
results of this paper rederives the existence of oscillatory motion in the
general N-body problem for N > 2.
