For Bedford-McMullen sponge systems with r coordinates, the metric mean dimension is a weighted sum of topological entropies of projections, and the mean Hausdorff dimension equals a weighted topological entropy divided by log m_1.
The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result
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Mean dimension theory for infinite dimensional Bedford-McMullen sponges
For Bedford-McMullen sponge systems with r coordinates, the metric mean dimension is a weighted sum of topological entropies of projections, and the mean Hausdorff dimension equals a weighted topological entropy divided by log m_1.