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arXiv · 2511.09451

When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$

Kevin G. Hare·Joaquin G. Prandi
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Abstract

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.

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Kevin G. Hare, Joaquin G. Prandi. 2025-11-12. When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$. https://arxiv.org/abs/2511.09451

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