On the Dynamical and Algebraic Properties of Bratteli Diagrams

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.