A topological classification for piecewise monotone iterative roots

Abstract

It is proved that every continuous iterative root of a piecewise monotone function with finite nonmonotonicity height, is an extension from a root on the characteristic interval. In this paper, a topological classification for those iterative roots is investigated. We first characterize all conjugacies between those piecewise monotone functions with finite nonmonotonicity height, and then determine a topological relation for their continuous iterative roots.