2024/10/25 by Hochman, Michael
#11J13 #11J83 #28A80 #37C45 #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2410.19640
We show that the Feng-Xiong lower bound of 1/2 for the box dimension of αβ-sets is tight. We also study how much of an αβ-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.