Derivative of the iterations of Minkowski question mark function in special points

2021/04/18 by Nikita Shulga, Shulga, Nikita
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2104.08897

11 pages

arxiv created 2021/04/20 · arxiv updated 2021/04/22

Abstract

For the Minkowski question mark function ?(x) we consider derivative of the function f_n(x) = \underbrace?(?(...?_n times(x))). Apart from obvious cases (rational numbers for example) it is non-trivial to find explicit examples of numbers x for which f'_n(x)=0. In this paper we present a set of irrational numbers, such that for every element x₀ of this set and for any n∈ℤ₊ one has f'_n(x₀)=0.

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