Ergodic theory studies measure-preserving
transformations of measure spaces. These objects are intrinsically infinite
and the notion of an individual point or an orbit makes no sense. Still there
is a variety of situations when a measure-preserving transformation (and its
asymptotic behavior) can be well described as a limit of certain finite objects
(periodic processes).
In the first part of this book this idea is developed systematically,
genericity of approximation in various categories is explored, and numerous
applications are presented, including spectral multiplicity and properties
of the maximal spectral type. The second part of the book contains a
treatment of various constructions of cohomological nature with an emphasis
on obtaining interesting asymptotic behavior from approximate pictures at
different time scales.
The book presents a view of ergodic theory not found in other expository
sources and is suitable for graduate students familiar with measure theory
and basic functional analysis.
Readership
Graduate students and research mathematicians interested in ergodic
theory.