Princeton University Press - The Plaid Model (AMS-198)

The Plaid Model (AMS-198) is a specialized mathematical text from Princeton University Press that explores the complexities of outer billiards. As a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, this volume provides a deep dive into a combinatorial model for orbits of outer billiards on kites. Outer billiards serves as a toy model for planetary motion, presenting behavior that is mysterious even in simple examples. This work examines a dynamical system where a particle moves around the outside of a convex shape using a scheme similar to ordinary billiards. Readers will find connections to various mathematical topics, including polytope exchange transformations, renormalization, and continued fractions. This book is an essential resource for those studying mathematical analysis, differential equations, and dynamical systems within the Annals of Mathematics Studies series.