When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918527266455552 |
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| author | Hare, Kevin G. Prandi, Joaquin G. |
| author_facet | Hare, Kevin G. Prandi, Joaquin G. |
| contents | Let $\mathcal{S}$ be an iterated function system in $\mathbb{R}^d$, with full support and some restrictions on the allowable rotations. We show that $\mathcal{S}$ satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. With this in mind, we extend the notion of net intervals from $\mathbb{R}$ to $\mathbb{R}^d$. We also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$ Hare, Kevin G. Prandi, Joaquin G. Dynamical Systems Let $\mathcal{S}$ be an iterated function system in $\mathbb{R}^d$, with full support and some restrictions on the allowable rotations. We show that $\mathcal{S}$ satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. With this in mind, we extend the notion of net intervals from $\mathbb{R}$ to $\mathbb{R}^d$. We also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support. |
| title | When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.09451 |