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.
General
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