AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

The Octagonal PETs
Richard Evan Schwartz, Brown University, Providence, RI
cover
SEARCH THIS BOOK:

Mathematical Surveys and Monographs
2014; 212 pp; hardcover
Volume: 197
ISBN-10: 1-4704-1522-4
ISBN-13: 978-1-4704-1522-8
List Price: US$90
Member Price: US$72
Order Code: SURV/197
[Add Item]

Request Permissions

Temporarily out of stock.
Expected date of availability is October 29, 2014.
See also:

Mostly Surfaces - Richard Evan Schwartz

Really Big Numbers - Richard Evan Schwartz

An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition - R Clark Robinson

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.

Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia