Omega-limit sets for shift spaces and unimodal maps

This paper investigates the structure of points u∈ANu∈AN that are such that the omega-limit set ω(u,σ)ω(u,σ) is precisely X  , where X⊆ANX⊆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)ω(c,f) is either a minimal Cantor set or properly contains a minimal Cantor set.