TY - JOUR
T1 - Mean dimension and a sharp embedding theorem
T2 - Extensions of aperiodic subshifts
AU - Gutman, Yonatan
AU - Tsukamoto, Masaki
N1 - Publisher Copyright:
© Cambridge University Press, 2013.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2013/4/3
Y1 - 2013/4/3
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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U2 - 10.1017/etds.2013.30
DO - 10.1017/etds.2013.30
M3 - Article
AN - SCOPUS:84938244609
VL - 34
SP - 1888
EP - 1896
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 6
ER -