Hölder exponents and fractal structure of level sets of self-affine functions associated with the $Q_s$-representation of numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915891014270976 |
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| author | Yelahin, Volodymyr Moroz, Mykola |
| author_facet | Yelahin, Volodymyr Moroz, Mykola |
| contents | We investigate a class of locally complicated self-affine functions defined via the $Q_s$-representation of real numbers. In particular, we compute local Hölder 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24411 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hölder exponents and fractal structure of level sets of self-affine functions associated with the $Q_s$-representation of numbers Yelahin, Volodymyr Moroz, Mykola Classical Analysis and ODEs Primary 28A80, Secondary 26A16, 26A27, 11K55 We investigate a class of locally complicated self-affine functions defined via the $Q_s$-representation of real numbers. In particular, we compute local Hölder 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. |
| title | Hölder exponents and fractal structure of level sets of self-affine functions associated with the $Q_s$-representation of numbers |
| topic | Classical Analysis and ODEs Primary 28A80, Secondary 26A16, 26A27, 11K55 |
| url | https://arxiv.org/abs/2603.24411 |