Outer billiards and the plaid model

Richard Schwartz, Brown University
Fine Hall 601

Outer billiards is a billiards-like dynamical system which is defined on the outside of a convex shape in the plane. Even for simple shapes, like kites (bilaterally symmetric quadrilaterals), the orbits have an intricate fractal-like structure. I'll explain a combinatorial model, which I call the plaid model, which gives a precise picture of that the outer billiards orbits look like on kites. This model explains, among other things, why the orbits have a (coarsely) self-similar structure in case the parameter associated to the kite is a quadratic irrational.