Geodesic
Hypercyclic Abelian Groups of Affine Maps on Cn
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 477-490

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2012-019-6
Mots-clés : 37C85, 47A16, affine, hypercyclic, dense, orbit, affine group, abelian 
Ayadi, Adlene. Hypercyclic Abelian Groups of Affine Maps on Cn. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 477-490. doi: 10.4153/CMB-2012-019-6
@article{10_4153_CMB_2012_019_6,
     author = {Ayadi, Adlene},
     title = {Hypercyclic {Abelian} {Groups} of {Affine} {Maps} on {Cn}},
     journal = {Canadian mathematical bulletin},
     pages = {477--490},
     year = {2013},
     volume = {56},
     number = {3},
     doi = {10.4153/CMB-2012-019-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-019-6/}
}
TY  - JOUR
AU  - Ayadi, Adlene
TI  - Hypercyclic Abelian Groups of Affine Maps on Cn
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 477
EP  - 490
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-019-6/
DO  - 10.4153/CMB-2012-019-6
ID  - 10_4153_CMB_2012_019_6
ER  - 
%0 Journal Article
%A Ayadi, Adlene
%T Hypercyclic Abelian Groups of Affine Maps on Cn
%J Canadian mathematical bulletin
%D 2013
%P 477-490
%V 56
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-019-6/
%R 10.4153/CMB-2012-019-6
%F 10_4153_CMB_2012_019_6

[1] [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] [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] [3] Bayart, F. and Matheron, E., Dynamics of Linear Operators. Cambridge Tracts in Math. 179, Cambridge University Press, 2009. Google Scholar

[4] [4] Javaheri, M., A generalization of Dirichlet approximation theorem for the affine actions on real line. J. Number Theory 128 (2008), 1146–1156. Google Scholar | DOI

[5] [5] Kulkarni, R. S., Dynamics of linear and affine maps. Asian J. Math. 12 (2008), 321–344. Google Scholar

[6] [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. Google Scholar | DOI

[7] [7] Waldschmidt, M., Topologie des points rationnels. Cours de Troisi`eme Cycle, Université P. et M. Curie (Paris VI), 1994/95. Google Scholar

Cité par Sources :