The octagonal PETs
Author(s)
Bibliographic Information
The octagonal PETs
（Mathematical surveys and monographs, v. 197）
American Mathematical Society, c2014
- Other Title
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The octogonal PETs
Available at / 30 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
S||MSM||197200029525488
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Note
Title of some printings: The octogonal PETs
Bibliography: p. 211-212
Description and Table of Contents
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.
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