New dimension bounds for $\alpha\beta$ sets
Dynamical Systems
2021-02-12 v1 Metric Geometry
Number Theory
Abstract
In this paper we obtain new lower bounds for the upper box dimension of sets. As a corollary of our main result, we show that if is not a Liouville number and is a Liouville number, then the upper box dimension of any set is . We also use our dimension bounds to obtain new results on affine embeddings of self-similar sets.
Cite
@article{arxiv.2102.05979,
title = {New dimension bounds for $\alpha\beta$ sets},
author = {Simon Baker},
journal= {arXiv preprint arXiv:2102.05979},
year = {2021}
}