  We give a complete characterization of the affine self-mappings $\varphi$ of
the torus $\mathbb T^d$ that generate K\"ohler-tame semicascades and cascades.
Namely, we show that the semicascade generated by $\varphi$ is tame if and only
if the matrix $A$ of $\varphi$ satisfies $A^p=A^q$, where $p$ and $q$ are some
nonnegative integers, $p\neq q$. For cascades the corresponding condition has
the form $A^m=I$, where $m$ is some positive integer and $I$ is the identity
matrix.
