
Preface  Introduction  Preview Material  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2014; 212 pp; hardcover Volume: 197 ISBN10: 1470415224 ISBN13: 9781470415228 List Price: US$90 Member Price: US$72 Order Code: SURV/197 See also: Mostly Surfaces  Richard Evan Schwartz Really Big Numbers  Richard Evan Schwartz An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition  R Clark Robinson  A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmüller 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 1parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semiregular octagons. The 1parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semiregular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computerassisted calculations. Readership Graduate students and research mathematicians interested in dynamical systems. 


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