On the history of the Ulam's Conjugacy

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