On the history of the Ulam's Conjugacy

Abstract

We show the results on the history of the invention of the conjugacy $h(x)=\frac{2}{\pi }\arcsin \sqrt{x}$ of one-dimensional $[0,1]\to [0,1]$ maps $f(x)=4x(1-x)$ and $g(x)=1-|1-2x|$.