Universal holomorphic maps with slow growth I. An Algorithm

We design an Algorithm to fabricate universal holomorphic maps between any two complex Euclidean spaces, within preassigned transcendental growth rate. As by-products, universal holomorphic maps from ${\mathbb{C}}^n$ to ${\mathbb{C}\mathbb{P}}^m$ ($n⩽m$) and to complex tori having slow growth are obtained. We take inspiration from Oka manifolds theory, Nevanlinna theory, and hypercyclic operators theory.