Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T18:49:38.088Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract.

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Ayadi, A. and Marzougui, H., Dense orbits for abelian subgroups of GL(n;C). In: Foliations 2005, World Sci. Publ., Hackensack, NJ, 2006, 47–69.Google Scholar
[2] Ayadi, A., Marzougui, H. and N'dao, Y., On the dynamic of abelian groups of affine maps on Cn and Rn. Preprint, ICTP, IC /2009/062, 2009.Google Scholar
[3] Bayart, F. and Matheron, E., Dynamics of Linear Operators. Cambridge Tracts in Math. 179, Cambridge University Press, 2009.Google Scholar
[4] Javaheri, M., A generalization of Dirichlet approximation theorem for the affine actions on real line. J. Number Theory 128 (2008), 1146–1156. http://dx.doi.org/10.1016/j.jnt.2007.08.008 Google Scholar
[5] Kulkarni, R. S., Dynamics of linear and affine maps. Asian J. Math. 12 (2008), 321–344.Google Scholar
[6] Bergelson, V., Misiurewicz, M. and Senti, S., Affine actions of a free semigroup on the real line. Ergodic Theory Dynam. Systems 26 (2006), 1285–1305. http://dx.doi.org/10.1017/S014338570600037X Google Scholar
[7] Waldschmidt, M., Topologie des points rationnels. Cours de Troisi`eme Cycle, Université P. et M. Curie (Paris VI), 1994/95.Google Scholar