Monotonic semiconjugacies onto expanding maps of the interval

Abstract

A contraction mapping is used to produce a semiconjugacy from a map τ 1 {\tau _1} with maximum at c 1 {c_1} to an expanding unimodal map with maximum at c 2 {c_2} under the assumption that there is an interval J J containing c 1 {c_1} such that there is a one-to-one, order-preserving correspondence between the orbit of J J under τ 1 {\tau _1} and the orbit of c 2 {c_2} under the expanding map.