2 problems

Let $(X,T)$ be a topological dynamical system, meaning that $(X,d)$ is a compact metric space and $T\colon X\to X$ is continuous. Assume that $(X,T)$ has zero topological entropy,…

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…