Abstract
We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.
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Dou, D., Park, K.K. Examples of entropy generating sequence. Sci. China Math. 54, 531–538 (2011). https://doi.org/10.1007/s11425-010-4152-y
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DOI: https://doi.org/10.1007/s11425-010-4152-y