Cantor Minimal Systems
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-4115-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4115-9 (ISBN)
Within 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.
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.
Ian F. Putnam, University of Victoria, BC, Canada.
An 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 notation
| Erscheinungsdatum | 01.08.2018 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 300 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-4115-2 / 1470441152 |
| ISBN-13 | 978-1-4704-4115-9 / 9781470441159 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Festigkeits- und Verformungslehre, Baudynamik, Wärmeübertragung, …
Buch | Hardcover (2025)
De Gruyter Oldenbourg (Verlag)
CHF 125,90
