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The Ellis semigroup of certain constant-length substitutions

Part of: Semigroups Connections with other structures, applications Topological dynamics

Published online by Cambridge University Press:  06 December 2019

PETRA STAYNOVA
PETRA STAYNOVA*
Affiliation:
University of Leeds Faculty of Mathematics and Physical Sciences, Mathematics, Mathematics, Leeds, LS2 9JT, UK email petra.staynova@gmail.com
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Abstract

In this article, we calculate the Ellis semigroup of a certain class of constant-length substitutions. This generalizes a result of Haddad and Johnson [IP cluster points, idempotents, and recurrent sequences. Topology Proc.22 (1997) 213–226] from the binary case to substitutions over arbitrarily large finite alphabets. Moreover, we provide a class of counterexamples to one of the propositions in their paper, which is central to the proof of their main theorem. We give an alternative approach to their result, which centers on the properties of the Ellis semigroup. To do this, we also show a new way to construct an almost automorphic–isometric tower to the maximal equicontinuous factor of these systems, which gives a more particular approach than the one given by Dekking [The spectrum of dynamical systems arising from substitutions of constant length. Z. Wahrscheinlichkeitstheor. Verw. Geb.41(3) (1977/78) 221–239].

Keywords

symbolic dynamicstilingstopological dynamics

MSC classification

Primary: 37B10: Symbolic dynamics 54H20: Topological dynamics
Secondary: 20M20: Semigroups of transformations, etc. 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 3 , March 2021 , pp. 935 - 960
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Copyright
© Cambridge University Press, 2019

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