New dimension bounds for αβ sets

[摘要] In this paper we obtain new lower bounds for the upper box dimension of alpha beta sets. As a corollary of our main result, we show that if a is not a Liouville number and alpha is a Liouville number, then the upper box dimension of any alpha beta set is 1. We also use our dimension bounds to obtain new results on affine embeddings of self-similar sets. Crown Copyright (C) 2021 Published by Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] alpha beta sets;Diophantine approximation;Self-similar sets