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arXiv · 2410.19640

On the dimension of $\alpha \beta$-sets

Michael Hochman
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Abstract

We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $\alpha\beta$-sets is tight. We also study how much of an $\alpha\beta$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times can cause the box dimension to drop to zero, but the Assouad dimension cannot drop below $1/4$.

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Michael Hochman. 2024-10-25. On the dimension of $\alpha \beta$-sets. https://arxiv.org/abs/2410.19640

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