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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.09255 |
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| _version_ | 1866909899413258240 |
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| author | Miao, Junjie Xu, Minghui |
| author_facet | Miao, Junjie Xu, Minghui |
| contents | Moran sets are a non-autonomous generalization of self-similar sets. In this paper, we study the quasi-Assouad and Assouad dimensions of Moran sets in $\mathbb{R}^{d}$. First we provide quasi-Assouad dimension formulae for Moran sets satisfying $c_*>0$. Then, we provide the upper and lower bounds for quasi-Assouad dimension formulae for Moran sets without assuming $c_*>0$. To obtain the exact dimension formulae in this case, we define quasi-normal and normal Moran sets, and provide quasi-Assouad dimension formulae for these sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Assouad and quasi-Assouad dimensions of Moran sets Miao, Junjie Xu, Minghui Dynamical Systems Moran sets are a non-autonomous generalization of self-similar sets. In this paper, we study the quasi-Assouad and Assouad dimensions of Moran sets in $\mathbb{R}^{d}$. First we provide quasi-Assouad dimension formulae for Moran sets satisfying $c_*>0$. Then, we provide the upper and lower bounds for quasi-Assouad dimension formulae for Moran sets without assuming $c_*>0$. To obtain the exact dimension formulae in this case, we define quasi-normal and normal Moran sets, and provide quasi-Assouad dimension formulae for these sets. |
| title | Assouad and quasi-Assouad dimensions of Moran sets |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.09255 |