Dynamical Systems Seminar- Introduction to billiards

Abstract: We will begin our discussion about the topic of the dynamics of billiards: Think of a billiard (i.e, pool) table whose boundary is a piecewise smooth simple closed curve. A ball moves (forever) around the interior, observing the angle of incidence equals angle of reflection rule each time it encounters the edge. Does the motion ever repeat (called periodic motion) or not? Does it go everywhere, or is it confined to a few parts of the table? How much time does it spend in one part of the table compared to another? I will begin with a general survey of what is known about these questions. Then we will switch to the special case of polygonal tables with rational angle corners. This is currently a very active research area related to “Teichmuller” theory. For the rest of the year, we will try to learn a little about it.