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Abelian Semigroups of Matrices on ℂn and Hypercyclicity

Published online by Cambridge University Press:  05 September 2013

Adlene Ayadi
Affiliation:
Department of Mathematics, Faculty of Science of Gafsa, University of Gafsa, Gafsa 2112, Tunisia, ([email protected])
Habib Marzougui
Affiliation:
Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Zarzouna 7021, Tunisia, ([email protected]; [email protected])
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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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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