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WAP systems and labeled subshifts. (English) Zbl 1455.37002

Memoirs of the American Mathematical Society 1265. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3761-9/pbk; 978-1-4704-5503-3/ebook). v, 116 p. (2019).
The survey deals with subshift systems in symbolic dynamics. Consider a symbolical dynamical system: \(S: A^{\mathbb Z}\to A^{\mathbb Z}\), \(S\) defining a shift transformation. Typically, a subshift \(B\) (i.e., a closed \(S\)-invariant subset of \(A^{\mathbb Z}\)) is uncountable. If \(B\) is countable, some nice theory can be built.
The main purpose of this work is to present a robust method to construct subshifts which are then used to build WAP (weakly almost periodic) systems with various properties. As an application of this strategy many examples are explicitly given and discussed.

MSC:

37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37B51 Multidimensional shifts of finite type
37B10 Symbolic dynamics
54H15 Transformation groups and semigroups (topological aspects)
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