  Polygonal slap maps are piecewise affine expanding maps of the interval
obtained by projecting the sides of a polygon along their normals onto the
perimeter of the polygon. These maps arise in the study of polygonal billiards
with non-specular reflections laws. We study the absolutely continuous
invariant probabilities of the slap maps for several polygons, including
regular polygons and triangles. We also present a general method for
constructing polygons with slap maps having more than one ergodic absolutely
continuous invariant probability.
