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arXiv · 2507.10982

Hausdorff dimensions of Beatty multiple shifts

Jung-Chao Ban·Wen-Guei Hu·Guan-Yu Lai
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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.

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Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai. 2025-07-15. Hausdorff dimensions of Beatty multiple shifts. https://arxiv.org/abs/2507.10982

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