Hausdorff dimensions of affine multiplicative shifts

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-04-09 DOI:10.1016/j.aim.2025.110266

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

引用次数: 0

Abstract

We calculate the Minkowski and Hausdorff dimensions of affine multiplicative shifts

X_{A}^{(p, q; a, b)} = {{(x_{i})}_{i = 1}^{\infty} \in {0, . . ., m - 1}^{N} : a_{x_{p k + a}, x_{q k + b}} = 1 for all k \geq 1},

where

1 \leq p < q \in N

a, b \in Z

1 \leq p + a < q + b

and

A = {[a_{i, j}]}_{i, j = 0}^{m - 1}

is an

m \times m

matrix with entries 0 or 1.

查看原文本刊更多论文

仿射乘移的豪斯多夫维数

我们计算了仿射乘法移位的Minkowski维数和Hausdorff维数xa (p,q;a,b)={(xi)i=1∞∈{0，…，m−1}N:axpk+a,xqk+b=1，对于所有k≥1}，其中1≤p<；q∈N, a,b∈Z, 1≤p+a<q+b, a =[ai,j]i,j=0m−1是一个元素为0或1的m×m矩阵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.