Suppose, I have a function $f(z)=\xi z$ where $|\xi|=1$ but $\xi$ is not a root of unity. Then, from the fact that the $n$-th iteration $f^{\circ n}(z)$, $z \in \mathbb{C}$, is dense on the circle around $0$ and radius $|z|$, how can I can deduce that $\{f^{\circ n}\}$ is a normal family?
Thanks for any help!