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arXiv · 2306.03047

A formula for the upper box-counting dimension of self-projective sets

Benedict Sewell
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Abstract

We prove a packing exponent formula for the upper box-counting dimension of attractors of certain projective iterated function systems. This partially affirms a conjecture of De Leo, and gives that the box-counting dimension of the Rauzy gasket $\mathcal R$, $\operatorname{dim}_B(\mathcal R)$, exists and satisfies $\operatorname{dim}_B(\mathcal R) = \operatorname{dim}_H(\mathcal R) \in [1.6196,1.7415].$

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Benedict Sewell. 2023-06-05. A formula for the upper box-counting dimension of self-projective sets. https://arxiv.org/abs/2306.03047

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