On the Dimension of αβ-Sets

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 arbitrarily small positive density set of times can cause the box dimension to drop to zero, but the Assouad dimension cannot drop below $1/5$.