Omega-limit sets for shift spaces and unimodal maps

Abstract

This paper investigates the structure of points u∈AN that are such that the omega-limit set ω(u,σ) is precisely X, where X⊆AN is an internally transitive shift space. We then use those results to study the possible structures of the omega-limit set of the turning point for a unimodal map. Examples are provided of unimodal maps f where no iterate of the turning point c is recurrent and ω(c,f) is either a minimal Cantor set or properly contains a minimal Cantor set.