Dynamics of tuples of matrices

Abstract

In this article we answer a question raised by N. Feldman in 2008 concerning the dynamics of tuples of operators on $\mathbb {R}^n$. In particular, we prove that for every positive integer $n\geq 2$ there exist $n$-tuples $(A_1, A_2, \dotsc ,A_n)$ of $n\times n$ matrices over $\mathbb {R}$ such that $(A_1, A_2, \ldots ,A_n)$ is hypercyclic. We also establish related results for tuples of $2\times 2$ matrices over $\mathbb {R}$ or $\mathbb {C}$ being in Jordan form.