Polygonal Billiards

The billiard system inside a polygon P has a very simple description: a point moves rectilinearly with the unit speed until it hits a side of P; there it instantaneously changes its velocity according to the rule "the angle of incidence equals the angle of reflection," and continues the rectilinear motion. If the point hits a corner, its further motion is not defined. (see Billiards in Bounded Convex Domains). From the point of view of the theory of dynamical systems, polygonal billiards provide an example of parabolic dynamics in which nearby trajectories diverge with subexponential rate.