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arXiv · 2603.24411

H\"older exponents and fractal structure of level sets of self-affine functions associated with the $Q_s$-representation of numbers

Volodymyr Yelahin·Mykola Moroz
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Abstract

We investigate a class of locally complicated self-affine functions defined via the $Q_s$-representation of real numbers. In particular, we compute local H\"older exponents at points with given asymptotic frequencies of digits in their $Q_s$-representation. Furthermore, we establish conditions under which these functions possess continuum level sets. Finally, for self-affine functions satisfying additional conditions, we describe the geometric structure of the set of maximum points and show that this set can be fractal.

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Volodymyr Yelahin, Mykola Moroz. 2026-03-25. H\"older exponents and fractal structure of level sets of self-affine functions associated with the $Q_s$-representation of numbers. https://arxiv.org/abs/2603.24411

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