HYPERCYCLIC ABELIAN SEMIGROUP OF MATRICES ON C^n AND R^n AND k-TRANSITIVITY (k >= 2)

Adlene Ayadi (1)

1 Systèmes dynamiques et combinatoire:99UR15-15

We prove that the minimal number of matrices 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 semigroup nitely generated by matrices on C^n or R^n is never k-transitive for k>= 2. These answer questions raised by Feldman and Javaheri.

Mots clés: Hypercyclic; Tuple of matrices; Semigroup; Subgroup; Dense orbit; Transitive; Semigroup action

Domaines: Systèmes dynamiques [math.DS]

Adlene Ayadi. HYPERCYCLIC ABELIAN SEMIGROUP OF MATRICES ON C^n AND R^n AND k-TRANSITIVITY (k >= 2). 2010. ⟨hal-00487257⟩