### Abstract

Furstenberg [Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory1 (1967), 1-49] calculated the Hausdorff and Minkowski dimensions of one-sided subshifts in terms of topological entropy. We generalize this to-subshifts. Our generalization involves mean dimension theory. We calculate the metric mean dimension and the mean Hausdorff dimension of-subshifts with respect to a subaction of. The resulting formula is quite analogous to Furstenberg's theorem. We also calculate the rate distortion dimension of-subshifts in terms of Kolmogorov-Sinai entropy.

Original language | English |
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Journal | Ergodic Theory and Dynamical Systems |

DOIs | |

Publication status | Accepted/In press - 2020 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Shinoda, M., & Tsukamoto, M. (Accepted/In press). Symbolic dynamics in mean dimension theory.

*Ergodic Theory and Dynamical Systems*. https://doi.org/10.1017/etds.2020.47