Classification of commutative pairs of surjective maps of interval, one of which is unimodal

Abstract

We introduce here a classification of unimodal maps [0, 1] → [0, 1], which commute with piecewise linear surjective mapsRemind that if continuous piecewise linear unimodal map g commutes with a nonconstant piecewise linear map ψ, which is not an iteration of g, then g is topologically conjugated with the tent map by piecewise linear conjugacy.We use the obtained classification to illustrate the mentioned fact. 1 2