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