Piecewise monotone mappings on an interval provide simple examples
of discrete dynamical systems whose behaviour can be very
complicated. These notes are concerned with the properties of the
iterates of such mappings. The material presented can be understood
by anyone who has had a basic course in (one-dimensional) real
analysis. The account concentrates on the topological (as opposed
to the measure theoretical) aspects of the theory of piecewise
monotone mappings. As well as offering an elementary introduction
to this theory, these notes also contain a more advanced treatment
of the problem of classifying such mappings up to topological
conjugacy.
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