Lecture 17 - Convex Billiards
One fun application of phase volume preservation in a dynamical system is billiards. The polygonal table introduced recently when developing toral flows is an example of a general class of dynamical systems called convex billiards. Today, we will describe the system and talk about its properties. One interesting aspect of a convex billiard (essentially the table is a convex domain in the plane) is that it always has periodic orbits of all orders. This may not be obvious, but we will define the tools that expose why. And in one particular case, that of an elliptic billiard, there is a curious side effect of the table; given a particular placement of a pocket and ball placement, one can aim anywhere and cannot miss making the shot. Makes for good betting odds, eh?