Hausdorff dimensions of Beatty multiplicative shifts

Jung Chao Ban; Wen Guei Hu; Guan Yu Lai

doi:10.1016/j.jmaa.2025.130298

Hausdorff dimensions of Beatty multiplicative shifts

Jung Chao Ban
, Wen Guei Hu
, Guan Yu Lai^*

^*此作品的通信作者

自然科學學科

National Chengchi University
National Taiwan University
Sichuan University

研究成果: 期刊稿件 › 文章 › 同行評審

摘要

We introduce the Beatty multiplicative shift, which is a generalization of the multiplicative shift of finite type (multiplicative SFT) Kenyon et al. (2012) [18] and the affine multiplicative shift Ban et al. (2025) [3] . We obtain the Hausdorff dimension and Minkowski dimension formulas. It turns out that the coefficients of the formula are closely related to the classical disjoint covering of the positive integers in number theory.

原文	英語
文章編號	130298
期刊	Journal of Mathematical Analysis and Applications
卷	557
發行號	2
DOIs	https://doi.org/10.1016/j.jmaa.2025.130298
出版狀態	已出版 - 15 05 2026

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© 2025 Elsevier Inc.

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10.1016/j.jmaa.2025.130298

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T1 - Hausdorff dimensions of Beatty multiplicative shifts

AU - Ban, Jung Chao

AU - Hu, Wen Guei

AU - Lai, Guan Yu

PY - 2026/5/15

Y1 - 2026/5/15

N2 - We introduce the Beatty multiplicative shift, which is a generalization of the multiplicative shift of finite type (multiplicative SFT) Kenyon et al. (2012) [18] and the affine multiplicative shift Ban et al. (2025) [3] . We obtain the Hausdorff dimension and Minkowski dimension formulas. It turns out that the coefficients of the formula are closely related to the classical disjoint covering of the positive integers in number theory.

AB - We introduce the Beatty multiplicative shift, which is a generalization of the multiplicative shift of finite type (multiplicative SFT) Kenyon et al. (2012) [18] and the affine multiplicative shift Ban et al. (2025) [3] . We obtain the Hausdorff dimension and Minkowski dimension formulas. It turns out that the coefficients of the formula are closely related to the classical disjoint covering of the positive integers in number theory.

KW - Affine multiplicative shifts

KW - Beatty sequence

KW - Disjoint cover

KW - Hausdorff dimension

KW - Minkowski dimension

KW - Multiplicative subshifts

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DO - 10.1016/j.jmaa.2025.130298

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VL - 557

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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M1 - 130298

ER -

Hausdorff dimensions of Beatty multiplicative shifts

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