For topological dynamical systems with abelian group , which admit an equicontinuous factor , the Ellis semigroup is an extension of by its subsemigroup of elements which preserve the fibres of . We establish methods to compute 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.
Cite this article
Johannes Kellendonk, Reem Yassawi, The Ellis semigroup of bijective substitutions. Groups Geom. Dyn. 16 (2022), no. 1, pp. 29–73DOI 10.4171/GGD/640