The Octagonal PETs (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
211
Utgivningsdatum
2014-07-30
Förlag
American Mathematical Society
Illustrationer
illustrations
Dimensioner
266 x 190 x 12 mm
Vikt
589 g
ISSN
0076-5376
ISBN
9781470415228

The Octagonal PETs

av Richard Evan Schwartz
Inbunden,  Engelska, 2014-07-30
1995
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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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Richard Evan Schwartz, Brown University, Providence, RI, USA

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