# セミナー

## 力学系セミナー

タイトル Symbolic dynamics in mean dimension 2020年1月8日 15:00～ 篠田 万穂 氏（Centre de Physique Théorique, Ecole Polytechnique） 慶應義塾大学理工学部 34棟402号室 Furstenberg (1967) calculated the Hausdorff and Minkowski dimensions of one-sided subshifts in terms of topological entropy. We generalize this to $\mathbb{Z}^2$-subshifts. Our generalization involves mean dimension theory. We calculate the metric mean dimension and mean Hausdorff dimension of $\mathbb{Z}^2$-subshifts with respect to a subaction of $\mathbb{Z}$. The resulting formula is quite analogous to Furstenberg's theorem. We also calculate the rate distortion dimension of $\mathbb{Z}^2$-subshifts in terms of Kolmogorov-Sinai entropy.