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Entropy dimension is an entropy-type quantity which takes values in $[0,1]$and classifies different levels of intermediate growth rate of complexity fordynamical systems. In this paper, we consider the complexity of skew productsof irrational rotations with Bernoulli systems, which can be viewed asdeterministic walks in random sceneries, and show that this class of models canhave any given entropy dimension by choosing suitable rotations for the basesystem.

Entropy dimension for Deterministic Walks in Random Sceneries