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.
| ISBN: | 9781470415228 |
| Publication date: | 30th July 2014 |
| Author: | Richard Evan Schwartz |
| Publisher: | American Mathematical Society |
| Format: | Hardback |
| Pagination: | 211 pages |
| Series: | Mathematical Surveys and Monographs |
| Genres: |
Mathematics Differential calculus and equations Geometry Topology |
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.
The Octogonal PETs features in the following genres: Mathematics, Differential calculus and equations, Geometry, Topology
Hardback. Not Available.
The Octogonal PETs was written by Richard Evan Schwartz and published by American Mathematical Society
The Octogonal PETs has 211 pages
Yes it is part of Mathematical Surveys and Monographs series