Dynamics of weighted translations on Orlicz spaces

TL;DR

This paper investigates the conditions under which weighted translation operators on Orlicz spaces over locally compact groups exhibit chaos and multiple recurrence, establishing a link between these dynamical properties.

Contribution

It provides necessary and sufficient conditions for chaos and topological multiple recurrence of weighted translation operators on Orlicz spaces.

Findings

Chaos implies multiple recurrence for these operators.

Conditions for chaos are characterized in terms of the weights and the Young function.

The results extend understanding of dynamical behavior on Orlicz spaces.

Abstract

Let $G$ be a locally compact group, and let $\Phi$ be a Young function. In this paper, we give sufficient and necessary conditions for weighted translation operators on the Orlicz space $L^\Phi(G)$ to be chaotic and topologically multiply recurrent. In particular, chaos implies multiple recurrence in our case.