2 problems

Let $T\colon X\to X$ be a continuous map of a compact metric space, and let $h_{\mathrm{top}}(T)$ denote its topological entropy. For every $\alpha\in[0,h_{\mathrm{top}}(T)]$, ther…

Let $m\in\mathbb N$, and let a minimal $\mathbb Z$-system mean a minimal dynamical system with a continuous $\mathbb Z$-action. Its maximal equicontinuous factor is the maximal fac…