Semigroups of matrices with dense orbits

Abstract

We give examples of $n\times n$ matrices $A$ and $B$ over the filed $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ such that for almost every column vector $x\in {\mathbb{K}}^n$, the orbit of $x$ under the action of the semigroup generated by $A$ and $B$ is dense in ${\mathbb{K}}^n$.

11 pages

Cited by in corpus (4)

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• On the minimal number of matrices which form a locally hypercyclic, non-hypercyclic tuple
• Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices
• Topological transitive Abelian subgrouns of GL(n,R)