ABSTRACT: Equidistribution of billiards in some (finite) polygons is a very active field of research. First we talk about our new results in this field. Then we switch to the other class of billiards in infinite polygons of finite area (like the ``halving staircase'') and prove equidistribution results for the first time in this class (as far as we know).
We explain the surprising differences between the equidistribution of infinite orbits in the two classes.
This is joint work with my two Ph.D. students M. Donders and Y. Yang, and with an old friend W.W.L. Chen (Sydney).