{"product_id":"9781470415228","title":"Octagonal PETs","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.","brand":"Richard Evan Schwartz","offers":[{"title":"Default Title","offer_id":46776498618686,"sku":"9781470415228","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470415228_e8c0b1d6-8f53-40f9-94f6-46adcdb0e3f7.jpg?v=1707476973","url":"https:\/\/exclusivebooks.co.za\/products\/9781470415228","provider":"Exclusive Books Online","version":"1.0","type":"link"}