Li-Yorke chaos of $C_{0}$-semigroups under the weak topology

Abstract

In this paper, we introduce and investigate the concept of Li-Yorke chaos for $C_0$-semigroups in Banach spaces endowed with the weak topology. We establish that, unlike Li-Yorke chaos under the norm topology, weak Li-Yorke chaos can occur in finite-dimensional spaces. Several fundamental properties of such semigroups are presented. Furthermore, we derive necessary and sufficient conditions for a $C_0$-semigroup to exhibit Li-Yorke chaos in the weak topology.