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OverviewWithin the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and a basic course in general topology. Full Product DetailsAuthor: Ian F. PutnamPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.300kg ISBN: 9781470441159ISBN 10: 1470441152 Pages: 184 Publication Date: 30 April 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsAn example: A tale of two equivalence relations Basics: Cantor sets and orbit equivalence Bratteli diagrams: Generalizing the example The Bratteli-Vershik model: Generalizing the example The Bratteli-Vershik model: Completeness Etale equivalence relations: Unifying the examples The $D$ invariant The Effros-Handelman-Shen theorem The Bratteli-Elliott-Krieger theorem Strong orbit equivalence The $D_m$ invariant The absorption theorem The classification of AF-equivalence relations The classification of $\mathbb{Z}$-actions Examples Bibliography Index of terminology Index of notationReviewsAuthor InformationIan F. Putnam, University of Victoria, BC, Canada. Tab Content 6Author Website:Countries AvailableAll regions |
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