The Ellis semigroup of bijective substitutions

Kellendonk, Johannes and Yassawi, Reem (2021). The Ellis semigroup of bijective substitutions. Groups, Geometry, and Dynamics, 16(1) pp. 29–73.

DOI: https://doi.org/10.4171/ggd/640

Abstract

For topological dynamical systems (X,T,σ) with abelian group T, which admit an equicontinuous factor π (X,T,σ), the Ellis semigroup E(X)</i> is an extension of Y by its subsemigroup E^fib(X)E^fib (X) of elements which preserve the fibres of π. We establish methods to compute E^fib(X)and use them to determine the Ellis semigroup of dynamical systems arising from primitive aperiodic bijective substitutions. As an application, we show that for these substitution shifts, the virtual automorphism group is isomorphic to the classical automorphism group.

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• Item ORO ID
• 83325
• Item Type
• Journal Item
• ISSN
• 1661-7207
• Keywords
• Ellis semigroup; substitution shifts
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2021 European Mathematical Society
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• Jisc Publications-Router
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