  Let $\mathcal{O}_{K}$ be the ring of integers of an imaginary quadratic field
$K$. Recently, Ji and Xie proved that every rational map $f \colon
\widehat{\mathbb{C}} \rightarrow \widehat{\mathbb{C}}$ of degree $d \geq 2$
whose multipliers all lie in $\mathcal{O}_{K}$ is a power map, a Chebyshev map
or a Latt\`{e}s map. Their proof relies on a result from non-Archimedean
dynamics obtained by Rivera-Letelier. In the present note, we show that one can
avoid using this result by considering a differential equation instead. Our
proof of Ji and Xie's result also applies to the case of entire maps. Thus, we
also show that every nonaffine entire map $f \colon \mathbb{C} \rightarrow
\mathbb{C}$ whose multipliers all lie in $\mathcal{O}_{K}$ is a power map or a
Chebyshev map.

Dynamical Systems;Complex Variables