Fractal analysis of Guthrie-Nymann's set and its generalisations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929472238780416 |
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| author | Pratsiovytyi, Mykola Karvatskyi, Dmytro |
| author_facet | Pratsiovytyi, Mykola Karvatskyi, Dmytro |
| contents | In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represented as a union of open intervals and a Cantor set having zero Lebesgue measure and a fractional Hausdorff dimension. Moreover, we extend the result to a countable family of Cantorvals with a similar structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractal analysis of Guthrie-Nymann's set and its generalisations Pratsiovytyi, Mykola Karvatskyi, Dmytro Dynamical Systems 40A05, 28A80, 11B05 In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represented as a union of open intervals and a Cantor set having zero Lebesgue measure and a fractional Hausdorff dimension. Moreover, we extend the result to a countable family of Cantorvals with a similar structure. |
| title | Fractal analysis of Guthrie-Nymann's set and its generalisations |
| topic | Dynamical Systems 40A05, 28A80, 11B05 |
| url | https://arxiv.org/abs/2405.16576 |