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dense orbit

Proceedings of the Edinburgh Mathematical Society (1)

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Abelian Semigroups of Matrices on ℂn and Hypercyclicity
Adlene Ayadi, Habib Marzougui
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 2 / June 2014

Published online by Cambridge University Press:

05 September 2013, pp. 323-338
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We give a complete characterization of a hypercyclic abelian semigroup of matrices on ℂn. For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over ℂ that form a hypercyclic abelian semigroup on ℂn. In particular, we show that no abelian semigroup generated by n matrices on ℂn can be hypercyclic.