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Preprints Archive: Abstract of IC2010059 (2010)

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Hypercyclic abelian semigroups of matrices on C^n

by Adlene Ayadi and Habib Marzougui

Document info: Pages 14, Figures 0.

We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on $\mathbb{C}^{n}$. For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over $\mathbb{C}$ which forms a hypercyclic abelian semigroup on ${\mathbb{C}}^{n}$. In particular, we show that no abelian semigroup generated by $n$ matrices on $\mathbb{C}^{n}$ can be hypercyclic.

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