TY - JOUR

T1 - Symbolic dynamics in mean dimension theory

AU - Shinoda, Mao

AU - Tsukamoto, Masaki

N1 - Publisher Copyright:
© 2020 The Author(s).

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1017/etds.2020.47

DO - 10.1017/etds.2020.47

M3 - Article

AN - SCOPUS:85086843555

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

ER -