This 2000 book provides a self-contained introduction to typical
properties of homeomorphisms. Examples of properties of
homeomorphisms considered include transitivity, chaos and
ergodicity. A key idea here is the interrelation between typical
properties of volume preserving homeomorphisms and typical
properties of volume preserving bijections of the underlying
measure space. The authors make the first part of this book very
concrete by considering volume preserving homeomorphisms of the
unit n-dimensional cube, and they go on to prove fixed point
theorems (Conley-Zehnder- Franks). This is done in a number of
short self-contained chapters which would be suitable for an
undergraduate analysis seminar or a graduate lecture course. Much
of this work describes the work of the two authors, over the last
twenty years, in extending to different settings and properties,
the celebrated result of Oxtoby and Ulam that for volume
homeomorphisms of the unit cube, ergodicity is a typical property.
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