具有代数平移的齐次迭代函数系统的维数

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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Recently by modifying the arguments of Varjú in [28], Rapaport and Varjú [24] showed that if <math>\n <semantics>\n <mrow>\n <msub>\n <mi>t</mi>\n <mn>1</mn>\n </msub>\n <mo>,</mo>\n <mtext>…</mtext>\n <mo>,</mo>\n <msub>\n <mi>t</mi>\n <mi>m</mi>\n </msub>\n </mrow>\n <annotation>$t_1,\\ldots, t_m$</annotation>\n </semantics></math> are rational numbers and <math>\n <semantics>\n <mrow>\n <mn>0</mn>\n <mo><</mo>\n <mi>λ</mi>\n <mo><</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$0<\\lambda <1$</annotation>\n </semantics></math>, then\n\n ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70222","citationCount":"0","resultStr":"{\"title\":\"Dimension of homogeneous iterated function systems with algebraic translations\",\"authors\":\"De-Jun Feng, Zhou Feng\",\"doi\":\"10.1112/jlms.70222\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <math>\\n <semantics>\\n <mi>μ</mi>\\n <annotation>$ \\\\mu$</annotation>\\n </semantics></math> be the self-similar measure associated with a homogeneous iterated function system <math>\\n <semantics>\\n <mrow>\\n <mi>Φ</mi>\\n <mo>=</mo>\\n <msubsup>\\n <mrow>\\n <mo>{</mo>\\n <mi>λ</mi>\\n <mi>x</mi>\\n <mo>+</mo>\\n <msub>\\n <mi>t</mi>\\n <mi>j</mi>\\n </msub>\\n <mo>}</mo>\\n </mrow>\\n <mrow>\\n <mi>j</mi>\\n <mo>=</mo>\\n <mn>1</mn>\\n </mrow>\\n <mi>m</mi>\\n </msubsup>\\n </mrow>\\n <annotation>$ \\\\Phi = \\\\lbrace \\\\lambda x + t_j \\\\rbrace _{j=1}^m$</annotation>\\n </semantics></math> on <math>\\n <semantics>\\n <mi>R</mi>\\n <annotation>$\\\\mathbb {R}$</annotation>\\n </semantics></math> and a probability vector <math>\\n <semantics>\\n <msubsup>\\n <mrow>\\n <mo>(</mo>\\n <msub>\\n <mi>p</mi>\\n <mi>j</mi>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <mrow>\\n <mi>j</mi>\\n <mo>=</mo>\\n <mn>1</mn>\\n </mrow>\\n <mi>m</mi>\\n </msubsup>\\n <annotation>$ (p_{j})_{j=1}^m$</annotation>\\n </semantics></math>, where <math>\\n <semantics>\\n <mrow>\\n <mn>0</mn>\\n <mo>≠</mo>\\n <mi>λ</mi>\\n <mo>∈</mo>\\n <mo>(</mo>\\n <mo>−</mo>\\n <mn>1</mn>\\n <mo>,</mo>\\n <mn>1</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$0\\\\ne \\\\lambda \\\\in (-1,1)$</annotation>\\n </semantics></math> and <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>t</mi>\\n <mi>j</mi>\\n </msub>\\n <mo>∈</mo>\\n <mi>R</mi>\\n </mrow>\\n <annotation>$t_j\\\\in \\\\mathbb {R}$</annotation>\\n </semantics></math>. 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引用次数: 0

摘要

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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Dimension of homogeneous iterated function systems with algebraic translations

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Dimension of homogeneous iterated function systems with algebraic translations

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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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.