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Abelian Semigroups of Matrices on ℂn and Hypercyclicity

Published online by Cambridge University Press:  05 September 2013

Adlene Ayadi  and
Habib Marzougui
Adlene Ayadi
Affiliation:
Department of Mathematics, Faculty of Science of Gafsa, University of Gafsa, Gafsa 2112, Tunisia, (adlenesoo@yahoo.fr)
Habib Marzougui
Affiliation:
Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Zarzouna 7021, Tunisia, (habib.marzougui@fsb.rnu.tn; hmarzoug@ictp.it)
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Abstract

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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.

Keywords

hypercyclicmatricesorbitdense orbitsemigroupabelianPrimary 37C8547A16
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 323 - 338
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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