2 problems

Finite-or-dense orbit conjecture. For every $x_0\in U$, the orbit $\mathcal O(f,x_0)$ is finite or dense in $U$.

Let $\ell$ be an integer, and let $G$ be an $\ell$-layered directed acyclic graph with layers $L_1,\ldots,L_\ell$, where every edge goes from $L_i$ to $L_{i+1}$. An $\ell$-layered…