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The Octogonal Pets: 197 (Mathematical Surveys and Monographs)

Geometry & Topology

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Description

About the Author Richard Evan Schwartz, Brown University, Providence, RI, USA Product Description 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.

Product Specifications

Format: Hardcover
ASIN: 1470415224
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 30 July 2014
Listed Since: 13 May 2014

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The Octogonal Pets: 197 (Mathematical Surveys and Monographs)

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