Title: Outer Billiards, the Penrose Kite, and the Neumann Problem
Speaker: Professor Rich Schwartz
Speaker Info: Brown University
Brief Description:
Special Note:
Abstract:
Outer billiards is a simple dynamical system, based on an arbitrarily chosen planar convex shape. It was introduced by B. Neumann in the 1950's. Some consider outer billiards to serve as a toy model for celestial mechanics. All along, one of the central questions about outer billiards has been: Can there be an outer billiards system with an unbounded orbit? I recently discovered that outer billiards, defined relative to the Penrose kite, has some unbounded orbits. The Penrose kite is the convex quadrilateral that appears in the Penrose tiling. In my talk I will present vivid computer evidence for the truth of this assertion, and also sketch a proof. The proof (still in progress) has to do with polygon exchange maps, dynamics in a number ring, and self-similar tilings.Date: Friday, January 12, 2007