Rotation sets for unimodal maps of the interval

Abstract

We relate the rotation interval ρ(f) of a unimodal map f of the interval with its kneading invariant K(f). In particular, we show that for any μ∈(0,12), there are kneading invariants νμ and νμ,hom such that ρ(f)=[μ,12] if and only if νμ⪯K(f)⪯νμ,hom.