The Octagonal PETs Hardback
by Richard Evan Schwartz
Part of the Mathematical Surveys and Monographs series
Hardback
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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Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:211 pages
- Publisher:American Mathematical Society
- Publication Date:30/07/2014
- Category:
- ISBN:9781470415228
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Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Hardback
- Pages:211 pages
- Publisher:American Mathematical Society
- Publication Date:30/07/2014
- Category:
- ISBN:9781470415228