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arXiv · 2310.06561

Universal holomorphic maps with slow growth II. functional analysis methods

Bin Guo·Song-Yan Xie
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Abstract

By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}. Next, we establish that, in the space of holomorphic maps from $\mathbb{C}^n$ to any connected Oka manifold $Y$, equipped with the compact-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 $Y=\mathbb{C}$.

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Bin Guo, Song-Yan Xie. 2023-10-10. Universal holomorphic maps with slow growth II. functional analysis methods. https://arxiv.org/abs/2310.06561

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