Iterative roots of PM functions extended from the characteristic interval

Abstract

In this paper we consider the problem of finding iterative roots of order less than the number of forts of continuous piecewise monotone(PM) functions with nonmonotonicity height greater than one. We present sufficient conditions to extend iterative roots of PM functions from the characteristic interval which determines the behavior of the function under iteration. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.