Yahya N'Dao
Abstract
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In this paper, we prove that the minimal number of affine maps on C^n, required to form a hypercyclic abelian semigroup on C^n is n+1. We also prove that the action of any abelian group finitely generated by affine maps on C^n, is never k-transitive for k>=2.
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In this paper, we prove that the minimal number of affine maps on C^n, required to form a hypercyclic abelian semigroup on C^n is n+1. We also prove that the action of any abelian group finitely generated by affine maps on C^n, is never k-transitive for k>=2.
Key concepts: Abelian group, Affine transformation, Mathematics, Semigroup, Transitive relation, Combinatorics, Discrete mathematics, Pure mathematics