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Complete regularity of Ellis semigroups of $\mathbb Z$-actions

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arxiv 2001.02751 v2 pith:3IXHPJVO submitted 2020-01-08 math.DS math.GR

Marcy Barge , Johannes Kellendonk This is my paper · ORCID
classification math.DSmath.GR
keywords ellismathbbproximalitybackwardforwardsemigroupactionasymptoticity
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abstract

It is shown that the Ellis semigroup of a $\mathbb Z$-action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$- or $\mathbb R$-action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

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  1. The Ellis semigroup of bijective substitutions

    math.DS 2019-08 conditional novelty 8.0 of 10

    For shifts generated by primitive aperiodic bijective substitutions, the Ellis semigroup is described as a Rees matrix semigroup over a structure group, up to an explicitly stated condition on generalised height.

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