  A right triangular billiard system is equivalent to the system of two
colliding particles confined in a one-dimensional box. In spite of their
seeming simplicity, no definite conclusion has been drawn so far concerning
their ergodic properties. To answer this question, we transform the dynamics of
the right triangular billiard system to a piecewise map and analytically prove
the broken ergodicity. The mechanism leading to the broken ergodicity is
discussed, and some numerical evidence corroborating our conclusion is
provided.
