A characterization of $\omega$-limit sets in subshifts of Baire space

Abstract

In this paper we consider the structure of $\omega$-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for $\omega$-limit sets fail in this context. Nevertheless, we obtain characterizations of $\omega$-limit sets in subshift of finite types and of attracting $\omega$-limit sets in subshifts of bounded type.