On the history of the Ulam's Conjugacy

TL;DR

This paper explores the historical development of Ulam's conjugacy, highlighting its origins and significance in the study of one-dimensional dynamical systems.

Contribution

It provides a detailed historical account of the invention and development of Ulam's conjugacy function for specific quadratic maps.

Findings

Traces the origin of Ulam's conjugacy.

Connects the conjugacy to key quadratic maps.

Highlights the mathematical significance of the 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 $[0,\, 1]\rightarrow [0,\, 1]$ maps $f(x)=4x(1-x)$ and $g(x)=1-|1-2x|$.