On the Dimension of αβ-Sets

Michael Hochman

doi:10.1093/imrn/rnaf186

On the Dimension of αβ-Sets

Michael Hochman^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the Feng-Xiong lower bound of for the box dimension of-sets is tight. We also study how much of an-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.

Original language	English
Article number	rnaf186
Journal	International Mathematics Research Notices
Volume	2025
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnaf186
State	Published - 1 Jul 2025

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On the Dimension of αβ-Sets

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