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Minimal systems of arbitrary large mean topological dimension

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Abstract

Let G be a countable amenable group and P a polyhedron. The mean topological dimension mdim(X,G) of a subshift X ⊂ P G is a real number satisfying 0 ≤ mdim(X,G) ≤ dim(P), where dim(P) denotes the usual topological dimension of P. We give a construction of minimal subshifts X ⊂ P G with mean topological dimension arbitrarily close to dim(P).

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  1. Section de Mathématiques, Université de Genève 2-4, rue du Lièvre, Case Postale 64, CH-1211, Genève 4, Suisse

    Fabrice Krieger

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  1. Fabrice Krieger
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Correspondence to Fabrice Krieger.

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Krieger, F. Minimal systems of arbitrary large mean topological dimension. Isr. J. Math. 172, 425–444 (2009). https://doi.org/10.1007/s11856-009-0081-2

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  • DOI: https://doi.org/10.1007/s11856-009-0081-2

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