Octagonal PETs
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A01=Richard Evan Schwartz
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Author_Richard Evan Schwartz
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Product details
- ISBN 9781470415228
- Weight: 456g
- Dimensions: 178 x 254mm
- Publication Date: 30 Jul 2014
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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.
Richard Evan Schwartz, Brown University, Providence, RI, USA
