Dynamics of tuples of matrices

Abstract

In this article we answer a question raised by N. Feldman in \cite{Feldman} 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 $(A_1, A_2, ..., A_n)$ of $n\times n$ matrices over $\mathbb{R}$ such that $(A_1, A_2, ..., A_n)$ is hypercyclic. We also establish related results for tuples of $2\times 2$ matrices over $\mathbb{R}$ or $\mathbb{C}$ being in Jordan form.