# Symbolic dynamics in mean dimension theory

Mao Shinoda, Masaki Tsukamoto

Research output: Contribution to journalArticlepeer-review

## Abstract

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

Original language English Unknown Journal Published - Oct 2 2019

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