2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127338In the one-parameter family of power-law maps of the form $f_a(x)=-|x|^α+a,$ $α>1,$ we give examples of mutually related dynamically determined quantities, depending on the parameter $a$, such that one is a Pick function of the following one. These Pick functions are extendable by reflection through the $(1,+\infty)$ half-axis and have completely monotone derivatives there.Dynamical Systems30C20, 37F45text