Chaotic translations on weighted Orlicz spaces

TL;DR

This paper characterizes when translation operators on weighted Orlicz spaces over locally compact groups are topologically transitive and chaotic, linking these properties to the blow-up/collapse condition and the density of periodic elements.

Contribution

It provides new characterizations for chaos and transitivity of translation operators on weighted Orlicz spaces, highlighting their equivalence to the blow-up/collapse property.

Findings

Transitivity is equivalent to the blow-up/collapse property.

Dense periodic elements imply transitivity.

Characterizations of chaos in weighted Orlicz spaces.

Abstract

Let $G$ be a locally compact group, $w$ be a weight on $G$ and $\Phi$ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^\Phi(G)$. In particular, transitivity is equivalent to the blow-up/collapse property in our case. Moreover, the dense set of periodic elements implies transitivity automatically.