On the history of the Ulam's Conjugacy

preprint2016arXivOpen access

Abstract

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

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