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Constructions of subshifts with positive topological entropy dimension

The notion of entropy dimension has been introduced to measure the subexponential complexity of zero entropy systems. In this work we present a general construction of a strictly ergodic subshift of topological entropy dimension $α$ for each $α\in (0,1)$. It is shown that the system satisfies some sort of regularity in the size of atoms and the first return time. Moreover, we modify the construction to obtain a variant system that is weakly mixing.