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arXiv · 2511.09255

Assouad and quasi-Assouad dimensions of Moran sets

Junjie Miao·Minghui Xu
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Abstract

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.

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Junjie Miao, Minghui Xu. 2025-11-12. Assouad and quasi-Assouad dimensions of Moran sets. https://arxiv.org/abs/2511.09255

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