The Octagonal PETs(English, Hardcover, Schwartz Richard Evan)

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The Octagonal PETs(English, Hardcover, Schwartz Richard Evan) is written by Schwartz Richard Evan and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470415224 (ISBN 10) and 9781470415228 (ISBN 13).

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.