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Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$ We give a characterization of hypercyclic abelian group
$\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$
is finitely generated, this characterization is explicit. We prove
in particular
that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.
Keywords:affine, hypercyclic, dense, orbit, affine group, abelian Categories:37C85, 47A16 |