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By means of hypercyclic operator theory, we complement our previous resultson hypercyclic holomorphic maps between complex Euclidean spaces having slowgrowth rates,by showing {\it abstract abundance} rather than {\it explicitexistence}. Next, we establish that, in the space of holomorphic maps from$\mathbb{C}^n$ to any connected Oka manifold $Y$, equipped with thecompact-open topology, there exists a {\em dense} subset consisting of common{\em frequently hypercyclic} elements for all nontrivial translation operators.To our knowledge, this is new even for $n=1$ and $Y=\mathbb{C}$.

Universal holomorphic maps with slow growth II. functional analysis methods