Disjoint hypercyclic weighted translations on groups

Abstract

Let $1\le p<\infty$, and let $G$ be a locally compact group. We characterize disjoint hypercyclic weighted translation operators on the Lebesgue space $L^p\left(G\right)$ in terms of the weight, the Haar measure, and the group element. Disjoint supercyclic, disjoint mixing, and dual disjoint hypercyclic weighted translation operators are also characterized.