闵可夫斯基问号函数在特殊点上的迭代导数

Pub Date : 2021-01-01 DOI:10.7169/facm/1966

N. Shulga

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引用次数: 0

摘要

对于Minkowski问号函数？（x）我们考虑函数fn（x）=？的导数？（？（…？｝｛｝n次（x）））。除了明显的情况（例如有理数）之外，找到f′n（x）=0的数字x的显式例子是不平凡的。本文给出了一组无理数，使得该集合的每个元素x0和任何n∈Z+都有f′n（x0）=0。

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On the derivative of iterations of the Minkowski question mark function at special points

For the Minkowski question mark function ?(x) we consider derivative of the function fn(x) = ?(?(...? } {{ } 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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