Hausdorff dimensions of Beatty multiple shifts
Dynamical Systems
2025-07-16 v1 Number Theory
Abstract
In this paper, the Beatty multiple shift is introduced, which is a generalization of the multiplicative shift of finite type (multiple SFT) [Kenyon, Peres and Solomyak, Ergodic Theory and Dynamical Systems, 2012] and the affine multiple shift [Ban, Hu, Lai and Liao, Advances in Mathematics, 2025]. The Hausdorff and Minkowski dimension formulas are obtained, and the coefficients of the formula is closely related to the classical disjoint covering of the positive integers in number theory.
Keywords
Cite
@article{arxiv.2507.10982,
title = {Hausdorff dimensions of Beatty multiple shifts},
author = {Jung-Chao Ban and Wen-Guei Hu and Guan-Yu Lai},
journal= {arXiv preprint arXiv:2507.10982},
year = {2025}
}