On the Dynamical and Algebraic Properties of Bratteli Diagrams
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Authors
MacVicar, Neil
Date
Type
thesis
Language
eng
Keyword
topological dynamics , dimension groups , irrational rotations , Bratteli diagrams , Bratteli-Vershik systems
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Abstract
A variety of dynamical systems, in topological and measurable settings, can be realized as Bratteli-Vershik systems. This document introduces the basic notions of Bratteli diagrams and provides detailed descriptions of Bratteli-Vershik models in both abstract and concrete settings. We also introduce the algebraic properties of Bratteli diagrams that interact with the dynamical realizations. In particular, we explore the dynamical and algebraic features of Bratteli diagrams derived from the action of an irrational rotation on the circle with a distinguished parameter that further cuts the partitions generated by the rotation.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.