I am interested to learn to what extent results on billiards in polygons have been extended to multiple balls. Assume the balls have equal radii and the same mass, the same initial speed, and all collisions are perfectly elastic, as depicted in this* image:
           Wikipedia image http://upload.wikimedia.org/wikipedia/commons/6/6d/Translational_motion.gif
To be specific, let me start with just the square table. For single particle billiards, it is well known that (1) a trajectory of rational slope that avoids the corners is periodic, and (2) a trajectory of irrational slope that avoids the corners will be "uniformly distributed" in the sense that it spends equal times in equal areas.

Are there analogous results for billiard systems of $n>1$ balls within a square?

Perhaps it is necessary to make some assumption concerning the size of the ball radii and the box dimensions?
           3 balls http://cs.smith.edu/%7Eorourke/MathOverflow/ThreeBalls.jpg
The literature I've seen on billiard dynamics does not explore this territory. Likely there are results in the literature, in which case pointers would be appreciated. Thanks!