Hypercyclic abelian semigroup of matrices on Cn and Rn and k-transitivity (k ≥ 2)
Keywords:Hypercyclic, Tuple of matrices, Semigroup, Subgroup, Dense orbit, Transitive, Semigroup action
AbstractWe prove that the minimal number of matrices on Cn required to forma hypercyclic abelian semigroup on Cn is n+1. We also prove that theaction of any abelian semigroup finitely generated by matrices on Cnor Rn is never k-transitive for k 2. These answer questions raised byFeldman and Javaheri.
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