A non-marker aperiodic inverse-limit system has mean dimension and dynamical dimension N, and embeds into the (3N+2)-dimensional cubical shift.
Shi,Finite mean dimension and marker property, Trans
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Dynamical dimension and shift embeddability without the marker property
A non-marker aperiodic inverse-limit system has mean dimension and dynamical dimension N, and embeds into the (3N+2)-dimensional cubical shift.