The Octagonal PETs - Hardcover

Richard Evan Schwartz

Hardcover

ISBN 10: 1470415224 ISBN 13: 9781470415228

Publisher: American Mathematical Society, 2014

Synopsis

A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmuller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.

About this title

About the Author

Richard Evan Schwartz, Brown University, Providence, RI, USA

About this edition

• Publisher: American Mathematical Society
• Publication date: 2014
• ISBN 10: 1470415224
• ISBN 13: 9781470415228
• Binding: Hardcover
• Edition number: 1
• Number of pages: 211