On periodicity and hypercyclic weighted translation operators

TL;DR

This paper explores the conditions under which weighted translation operators with periodic elements are hypercyclic, utilizing a generalized form of Weyl's equidistribution theorem to establish necessary criteria.

Contribution

It introduces a generalized approach to analyze hypercyclicity of weighted translation operators with periodic elements, expanding understanding of their dynamic properties.

Findings

Identifies necessary conditions for hypercyclicity

Utilizes generalized Weyl's equidistribution theorem

Characterizes periodic elements in weighted translation operators

Abstract

We use the generization of Weyl's equidistribution theorem to characterize several necessary conditions of hypercyclic weighted translation operators with periodic element.