Mean dimension and a sharp embedding theorem: Extensions of aperiodic subshifts

Yonatan Gutman; Masaki Tsukamoto

doi:10.1017/etds.2013.30

Mean dimension and a sharp embedding theorem: Extensions of aperiodic subshifts

Yonatan Gutman, Masaki Tsukamoto

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We show that if (X, T) is an extension of an aperiodic subshift (a subsystem of ({ 1, 2, ⋯, l}^Z, shift ) for some l∈ N) and has mean dimension mdim (X, T)< (D/ 2), D∈ N, then it can be equivariantly embedded in [0, 1]^D)^Z, shift ). The result is sharp. If (X, T) is an extension of an aperiodic zero-dimensional system then it can be equivariantly embedded in [0, 1] ^{D+ 1})Z, shift).

Original language	English
Pages (from-to)	1888-1896
Number of pages	9
Journal	Ergodic Theory and Dynamical Systems
Volume	34
Issue number	6
DOIs	https://doi.org/10.1017/etds.2013.30
Publication status	Published - Apr 3 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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N2 - We show that if (X, T) is an extension of an aperiodic subshift (a subsystem of ({ 1, 2, ⋯, l}Z, shift ) for some l∈ N) and has mean dimension mdim (X, T)< (D/ 2), D∈ N, then it can be equivariantly embedded in [0, 1]D)Z, shift ). The result is sharp. If (X, T) is an extension of an aperiodic zero-dimensional system then it can be equivariantly embedded in [0, 1] D+ 1)Z, shift).

AB - We show that if (X, T) is an extension of an aperiodic subshift (a subsystem of ({ 1, 2, ⋯, l}Z, shift ) for some l∈ N) and has mean dimension mdim (X, T)< (D/ 2), D∈ N, then it can be equivariantly embedded in [0, 1]D)Z, shift ). The result is sharp. If (X, T) is an extension of an aperiodic zero-dimensional system then it can be equivariantly embedded in [0, 1] D+ 1)Z, shift).

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