2 problems

Let $(X,T)$ be a minimal topological dynamical system, meaning that for every $x\in X$, the set $\{T^n x\}$ is dense, with zero entropy. Let $x_0\in X$, let $f\in C(X)$, and let…

Let $s\in\mathbb{N}$, let $G/\Gamma$ be an $s$-step nilmanifold, where $G$ is a connected, simply connected $s$-step nilpotent Lie group and $\Gamma$ is a cocompact discrete subgro…