Mathematical Surveys and Monographs
Volume: 197; 2014; 212 pp; Hardcover
MSC: Primary 37;
Print ISBN: 978-1-4704-1522-8
Product Code: SURV/197
List Price: $90.00
AMS Member Price: $72.00
MAA Member Price: $81.00

Add to Cart (PRINT)

Electronic ISBN: 978-1-4704-1718-5
Product Code: SURV/197.E
List Price: $90.00
AMS Member Price: $72.00
MAA Member Price: $81.00

Supplemental Materials

The Octagonal PETs

Share this page

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.

Readership

Graduate students and research mathematicians interested in dynamical systems.

The Octagonal PETs

Base Product Code Keyword List: surv; SURV; surv/197; SURV/197; surv-197; SURV-197

Print Product Code: SURV/197

Online Product Code: SURV/197.E

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

Online Price 1 Label: List

Online Price 1: 90.00

Print Price 1 Label: List

Print Price 1: 90.00

Online Price 2 Label: AMS Member

Online Price 2: 72.00

Print Price 2 Label: AMS Member

Print Price 2: 72.00

Online Price 3 Label: MAA Member

Online Price 3: 81.00

Print Price 3 Label: MAA Member

Print Price 3: 81.00

Dual Price 1 Label: List

Dual Price 1: 112.5

Dual Price 2 Label: AMS Member

Dual Price 2: 90

Print Add to Cart URL: /some/url/at/AMS/SURV-197

Electronic Add to Cart URL: /some/url/at/AMS/SURV-197.E

Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1718-5&pisbn=978-1-4704-1522-8&epc=SURV/197.E&ppc=SURV/197&title=The%20Octagonal%20PETs&author=Richard%20Evan%20Schwartz&type=R

Readership:

Graduate students and research mathematicians interested in dynamical systems.

Free Attachments

Attachments

Follow Link Download FULL PDF Version

Cover
- Cover
Title page
- Title page
Contents
- Contents
Preface
- Preface
Chapter 1. Introduction
- Chapter 1. Introduction
Chapter 2. Background
- Chapter 2. Background

You may also like

Supplemental Materials

The Octagonal PETs

Readership

Table of Contents

Search

Table of Contents

The Octagonal PETs

Free Attachments

Attachments

Cover

Title page

Contents

Preface

Chapter 1. Introduction

Chapter 2. Background