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Hypercyclic Abelian Groups of Affine Maps on ℂn

Published online by Cambridge University Press:  20 November 2018

Adlene Ayadi
Adlene Ayadi*
Affiliation:
Department of Mathematics, Faculty of Sciences of Gafsa, University of Gafsa, Gafsa, Tunisia e-mail: adlenesoo@yahoo.com
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Abstract.

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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

37C8547A16affinehypercyclicdenseorbitaffine groupabelian
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 477 - 490
Copyright
Copyright © Canadian Mathematical Society 2013

References

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