Hausdorff dimensions of affine multiplicative shifts

Jung-Chao Ban; Wen-Guei Hu; Guan-Yu Lai; Lingmin Liao

doi:10.1016/j.aim.2025.110266

Hausdorff dimensions of affine multiplicative shifts

Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai, Lingmin Liao

Division of Natural Science

Research output: Contribution to journal › Journal Article › peer-review

Abstract

We calculate the Minkowski and Hausdorff dimensions of affine multiplicative shifts X _A ^(p,q;a,b)={(x _i) _i=1 ^∞∈{0,…,m−1} ^N:a _{x
_pk+a,x
_qk+b}=1 for all k≥1}, where 1≤p<q∈N, a,b∈Z, 1≤p+a<q+b and A=[a _i,j] _i,j=0 ^m−1 is an m×m matrix with entries 0 or 1.

Original language	English
Article number	110266
Journal	Advances in Mathematics
Volume	471
DOIs	https://doi.org/10.1016/j.aim.2025.110266
State	Published - 06 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier Inc.

Keywords

Affine multiplicative shifts
Hausdorff dimension
Minkowski dimension
Multiplicative subshifts

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10.1016/j.aim.2025.110266

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title = "Hausdorff dimensions of affine multiplicative shifts",

abstract = "We calculate the Minkowski and Hausdorff dimensions of affine multiplicative shifts X A (p,q;a,b)=\{(x i) i=1 ∞∈\{0,…,m−1\} N:a x pk+a,x qk+b =1 for all k≥1\}, where 1≤pi,j] i,j=0 m−1 is an m×m matrix with entries 0 or 1.",

keywords = "Affine multiplicative shifts, Hausdorff dimension, Minkowski dimension, Multiplicative subshifts",

author = "Jung-Chao Ban and Wen-Guei Hu and Guan-Yu Lai and Lingmin Liao",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2025",

month = jun,

doi = "10.1016/j.aim.2025.110266",

language = "英语",

volume = "471",

journal = "Advances in Mathematics",

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AU - Ban, Jung-Chao

AU - Hu, Wen-Guei

AU - Lai, Guan-Yu

AU - Liao, Lingmin

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Y1 - 2025/6

N2 - We calculate the Minkowski and Hausdorff dimensions of affine multiplicative shifts X A (p,q;a,b)={(x i) i=1 ∞∈{0,…,m−1} N:a x pk+a,x qk+b =1 for all k≥1}, where 1≤pi,j] i,j=0 m−1 is an m×m matrix with entries 0 or 1.

AB - We calculate the Minkowski and Hausdorff dimensions of affine multiplicative shifts X A (p,q;a,b)={(x i) i=1 ∞∈{0,…,m−1} N:a x pk+a,x qk+b =1 for all k≥1}, where 1≤pi,j] i,j=0 m−1 is an m×m matrix with entries 0 or 1.

KW - Affine multiplicative shifts

KW - Hausdorff dimension

KW - Minkowski dimension

KW - Multiplicative subshifts

UR - https://www.scopus.com/pages/publications/105002120528

U2 - 10.1016/j.aim.2025.110266

DO - 10.1016/j.aim.2025.110266

M3 - 文章

SN - 0001-8708

VL - 471

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 110266

ER -

Hausdorff dimensions of affine multiplicative shifts

Abstract

Bibliographical note

Keywords

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