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

Abstract

We introduce here a classification of unimodal maps $[0,1]\to [0,1]$, which commute with piecewise linear surjective maps $[0,1]\to [0,1]$. Remind that if continuous piecewise linear unimodal map $g$ commutes with a non-constant piecewise linear map $\psi$, 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.

46 pages, 19 figures