One-parameter families of functions in the Pick class
Abstract
Description
In 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.