Mathematical Surveys and Monographs
Volume: 197; 2014; 212 pp; Hardcover
MSC: Primary 37;
Print ISBN: 978-1-4704-1522-8
Product Code: SURV/197
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Electronic ISBN: 978-1-4704-1718-5
Product Code: SURV/197.E
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The Octagonal PETs

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Richard Evan Schwartz

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 Teichmüller 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.

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Graduate students and research mathematicians interested in dynamical systems.

The Octagonal PETs

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Print Product Code: SURV/197

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Title (HTML): The Octagonal PETs

Author(s) (Product display): Richard Evan Schwartz

Affiliation(s) (HTML): Brown University, Providence, RI

Abstract:

Book Series Name: Mathematical Surveys and Monographs

Volume: 197

Publication Month and Year: 2014-07-03

Page Count: 212

Cover Type: Hardcover

Print ISBN-13: 978-1-4704-1522-8

Online ISBN 13: 978-1-4704-1718-5

Print ISSN: 0076-5376

Online ISSN: 0076-5376

Primary MSC: 37

Textbook?: false

Applied Math?: false

MAA Book?: false

Electronic Media?: false

Apparel or Gift: false

SXG Subject: GT; DE

Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/surv-197

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Graduate students and research mathematicians interested in dynamical systems.

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Contents
- Contents
Preface
- Preface
Chapter 1. Introduction
- Chapter 1. Introduction
Chapter 2. Background
- Chapter 2. Background

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The Octagonal PETs

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The Octagonal PETs

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Cover

Title page

Contents

Preface

Chapter 1. Introduction

Chapter 2. Background