DOI: 10.1063/5.0349385 ISSN: 0022-2488

On directional entropy dimension of Z2-measure preserving systems

Chunlin Liu, Qian Zhang
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We introduce and develop the notion of directional entropy dimension for measure preserving Z2-actions. We establish a partial variational principle relating the measure theoretic and topological directional entropy dimensions. Using deterministic walks in random sceneries and product constructions, we construct examples showing that every value in the interval [0, 1] can be realized as the directional metric entropy dimension.

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