Extension of iterative roots

Abstract

This paper gives a purely set-theoretical extension theorem on iterative roots, which generalizes the results about PM functions by Zhang and his collaborators. Applying this extension theorem, we construct all iterative roots with infinitely many discontinuities for a class of Markov maps.Mathematics Subject Classification (2010). Primary 39B52; Secondary 39B82.

Topological conjugacy of piecewise monotonic functions of nonmonotonicity height ≥1

“…However, to apply the construction method in his paper, one of the major requirements was that these maps must be piecewise expanding. Later, some results were developed in [20,18,19,15,16]. Recently, further investigations to construct continuous iterative roots of PM functions were made in [11,10].…”