Examples of hypercyclic shifts in weighted spaces on graphs

Abstract

Shift operators play a special role in linear dynamics since very often they serve as examples of operators with chaotic behaviour (hypercyclicity, weak mixing, mixing). For the case of ordinary weighted sequence spaces $\ell^p(\mathbb{N},\mu)$ or $\ell^p(\mathbb{Z},\mu)$, hypercyclic shift operators were described by G.Salas in 1995. Recently the dynamics of operators on graphs has attracted a great interest. Hypercyclic shift operators on trees were described by K.Grosse-Erdmann and D.Papathanasiou in 2023. The first results for graphs that are not trees were obtained in a recent preprint by A.D.Baranov, A.A.Lishanskii and D.Papathanasiou. In this article we consider new examples of hypercyclic shifts on graphs.