Hypercyclicity and k-Transitivity (k>=2) for abelian semigroup of affine maps on Cⁿ

2013/09/06 by Yahya N'Dao, N'Dao, Yahya · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Geometric and Algebraic Topology #math.DS

paper · pdf · doi:10.48550/arxiv.1309.1760

arXiv admin note: substantial text overlap with arXiv:1309.1725

arxiv created 2013/09/06 · arxiv updated 2013/09/10

Abstract

In this paper, we prove that the minimal number of affine maps on Cⁿ, required to form a hypercyclic abelian semigroup on Cⁿ is n+1. We also prove that the action of any abelian group finitely generated by affine maps on Cⁿ, is never k-transitive for k>=2.

Citations

• Hypercyclic abelian semigroups of affine maps on Cⁿ

Cited by

• J-class of finitely generated abelian semigroups of affine mpas on Cⁿ and Hypercyclicity

Related

• Hypercyclic abelian semigroups of affine maps on Cⁿ
• Hypercyclic Abelian Affine Groups
• J-class of finitely generated abelian semigroups of affine mpas on Cⁿ and Hypercyclicity
• The C*-algebra of an affine map on the 3-torus
• Hypercyclic tuples of operators on Cⁿ and Rⁿ