The Octagonal PETs PDF
by Richard Evan Schwartz
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 Teichmueller 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.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:212 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470417185
Other Formats
- Hardback from £113.00
Information
-
Download - Immediately Available
- Format:PDF
- Pages:212 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470417185