no code implementations • 20 Feb 2021 • Lei Jin, Yixiao Qiao
However, there is still one longstanding problem which remains open in this direction, asking if there exists a continuous action of $G$ on some compact metrizable space $X$ such that $\mathrm{mdim}(X\times X, G)<2\cdot\mathrm{mdim}(X, G)$.
Dynamical Systems
no code implementations • 20 Feb 2021 • Lei Jin, Yixiao Qiao
We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0, 1]^\mathbb{Z}$.
Dynamical Systems
no code implementations • 5 Jan 2021 • Lei Jin, Kyewon Koh Park, Yixiao Qiao
For every infinite (countable discrete) amenable group $G$ and every positive integer $d$ we construct a minimal $G$-action of mean dimension $d/2$ which cannot be embedded in the full $G$-shift on $([0, 1]^d)^G$.
Dynamical Systems
