Hausdorff dimension for the weighted products of multiple digits in d-decaying Gauss like systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915648695697408 |
|---|---|
| author | Bakhtawar, Ayreena Rams, Michał |
| author_facet | Bakhtawar, Ayreena Rams, Michał |
| contents | We compute the Hausdorff dimension of sets defined by the growth of weighted products of multiple digits at arbitrary positions in $d$-decaying Gauss-like iterated function systems. We provide the complete Hausdorff dimensional result for product of more than two digits, which was an open problem even for consecutive digits in the classical Gauss map and Lüroth map. In our approach we do not need to assume the Bounded Distortion Property (BDP). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hausdorff dimension for the weighted products of multiple digits in d-decaying Gauss like systems Bakhtawar, Ayreena Rams, Michał Dynamical Systems Number Theory We compute the Hausdorff dimension of sets defined by the growth of weighted products of multiple digits at arbitrary positions in $d$-decaying Gauss-like iterated function systems. We provide the complete Hausdorff dimensional result for product of more than two digits, which was an open problem even for consecutive digits in the classical Gauss map and Lüroth map. In our approach we do not need to assume the Bounded Distortion Property (BDP). |
| title | Hausdorff dimension for the weighted products of multiple digits in d-decaying Gauss like systems |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2512.02641 |