Dimension of homogeneous iterated function systems with algebraic translations

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-04 DOI:10.1112/jlms.70222

De-Jun Feng, Zhou Feng

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引用次数: 0

Abstract

Let $μ$ be the self-similar measure associated with a homogeneous iterated function system $Φ = {λ x + t_{j}}_{j = 1}^{m}$ on $R$ and a probability vector ${(p_{j})}_{j = 1}^{m}$ , where $0 \neq λ \in (- 1, 1)$ and $t_{j} \in R$ . Recently by modifying the arguments of Varjú in [28], Rapaport and Varjú [24] showed that if $t_{1}, …, t_{m}$ are rational numbers and $0 < λ < 1$ , then

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具有代数平移的齐次迭代函数系统的维数

设μ $ \mu$为与齐次迭代函数系统相关的自相似测度Φ = {λ x + t j}j = 1 m $ \Phi = \lbrace \lambda x + t_j \rbrace _{j=1}^m$在R $\mathbb {R}$上和一个概率向量（p j） j = 1 m $ (p_{j})_{j=1}^m$，其中0≠λ∈(−1)，1) $0\ne \lambda \in (-1,1)$, t j∈R $t_j\in \mathbb {R}$。最近，Rapaport和Varjú[24]通过修改[28]中Varjú的参数表明，如果t 1，…T m $t_1,\ldots, t_m$为有理数，0 ＆lt；λ ＆lt；1 $0<\lambda <1$，那么

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.