Furstenberg (1967) calculated the Hausdorff and Minkowski dimensions of one-sided subshifts in terms of topological entropy. We generalize this to Z2-subshifts. Our generalization involves mean dimension theory. We calculate the metric mean dimension and mean Hausdorff dimension of Z2-subshifts with respect to a subaction of Z. The resulting formula is quite analogous to Furstenberg’s theorem. We also calculate the rate distortion dimension of Z2-subshifts in terms of Kolmogorov–Sinai entropy.
37A05, 37B10, 37C45, 94A34
|Publication status||Published - Oct 2 2019|
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