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

الأصل · EN

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.