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The Octagonal PETs
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Bibliographic Detail
Publisher Amer Mathematical Society
Publication date July 24, 2014
Pages 212
Binding Hardcover
Book category Adult Non-Fiction
ISBN-13 9781470415228
ISBN-10 1470415224
Dimensions 0.50 by 7.50 by 10.50 in.
Weight 1.30 lbs.
Original list price $90.00
Summaries and Reviews description: 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.

Book cover for 9781470415228
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from Amer Mathematical Society (July 24, 2014)
9781470415228 | details & prices | 212 pages | 7.50 × 10.50 × 0.50 in. | 1.30 lbs | List price $90.00
About: A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined.

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