Masaki Tsukamoto

collaborators

3 papers

math.DS2025

Rate distortion dimension and ergodic decomposition for $R^{d}$ -actions

Masaki Tsukamoto

Rate distortion dimension describes the theoretical limit of lossy data compression methods as the distortion bound goes to zero. It was originally introduced in the context of inf…

math.DS2023

Application of waist inequality to entropy and mean dimension: II

Masaki Tsukamoto

Let $X$ be a full-shift on the alphabet $[0, 1]^{a}$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that any equivariant continuous map from $X$ to $Y$ has conditional m…

math.DS2023

Variational principle for mean dimension with potential of $R^{d}$ -actions: I

Masaki Tsukamoto

We develop a variational principle for mean dimension with potential of $R^{d}$ -actions. We prove that mean dimension with potential is bounded from above by the supremum of…

Rate distortion dimension and ergodic decomposition for Rd-actions

Application of waist inequality to entropy and mean dimension: II

Variational principle for mean dimension with potential of Rd-actions: I

Rate distortion dimension and ergodic decomposition for $R^{d}$ -actions

Variational principle for mean dimension with potential of $R^{d}$ -actions: I