The partial derivative of Okamoto's functions with respect to the parameter

Abstract: Okamoto's functions were introduced in 2005 as a one-parameter family of self-affine functions, which are expressed by ternary expansion of $x$ on the interval $[0,1]$. By changing the parameter, one can produce interesting examples: Perkins' nowhere differentiable function, Bourbaki-Katsuura function and Cantor's Devil's staircase function.

In this talk, we consider the partial derivative of Okomoto's functions with respect to the parameter $a$. We place a significant focus on $a = 1/3$ to describe the properties of a nowhere differentiable function $K(x)$ for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension 1.

This is a joint work with T. Mathis and M.Paizanis (undergraduate students) and N.Dalaklis (graduate student). The talk is very accessible and includes many computer graphics.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

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