On faithfulness and DP-transformations generated by arithmetic Cantor series expansions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909987612131328 |
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| author | Torbin, Grygoriy Voloshyn, Yuliia |
| author_facet | Torbin, Grygoriy Voloshyn, Yuliia |
| contents | The paper is devoted to the study of conditions for the Hausdorff-Besicovitch faithfulness of the family of cylinders generated by Cantor series expansions. We show that there exist subgeometric Cantor series expansions for which the corresponding families of cylinders are not faithful for the Hausdorff-Besicovitch dimension on the unit interval. On the other hand we found a rather wide subfamily of subgeometric Cantor series expansions generating faithful families of cylinders.
We also study conditions for the Hausdorff-Besicovitch dimension preservation on [0;1] by probability distribution functions of random variables with independent symbols of arithmetic Cantor series expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On faithfulness and DP-transformations generated by arithmetic Cantor series expansions Torbin, Grygoriy Voloshyn, Yuliia Dynamical Systems Number Theory 11K55, 28A80, 60G30 The paper is devoted to the study of conditions for the Hausdorff-Besicovitch faithfulness of the family of cylinders generated by Cantor series expansions. We show that there exist subgeometric Cantor series expansions for which the corresponding families of cylinders are not faithful for the Hausdorff-Besicovitch dimension on the unit interval. On the other hand we found a rather wide subfamily of subgeometric Cantor series expansions generating faithful families of cylinders. We also study conditions for the Hausdorff-Besicovitch dimension preservation on [0;1] by probability distribution functions of random variables with independent symbols of arithmetic Cantor series expansions. |
| title | On faithfulness and DP-transformations generated by arithmetic Cantor series expansions |
| topic | Dynamical Systems Number Theory 11K55, 28A80, 60G30 |
| url | https://arxiv.org/abs/2601.07285 |