The Octagonal PETs (Hardcover)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Mathematical Surveys and Monographs
Release date:	July 2014
Authors:	Richard Evan Schwartz
Dimensions:	254 x 178mm (L x W)
Format:	Hardcover
Pages:	211
ISBN-13:	978-1-4704-1522-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > General
LSN:	1-4704-1522-4
Barcode:	9781470415228

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