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Let $C, D \subseteq \C$ with $z \in C \implies z + 1 \in C$.

Let $F: C \to D$ and $H: D \to D$ be holomorphic functions.

Let $\map H {\map F z} = \map F {z + 1}$ for all $z \in C$.

Then $F$ is said to be a superfunction of $H$, and $H$ is called a transfer function of $F$.

That is, superfunctions are iterations of transfer functions.

Also see


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