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.



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 Efib(X)Efib (X) of elements which preserve the fibres of π. We establish methods to compute Efib(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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