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On the dimension of $αβ$-sets
Published 25 Oct 2024 in math.DS and math.MG | (2410.19640v1)
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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