{"title":"具有非空内部的典型自阿芬集合","authors":"De-Jun Feng, Zhou Feng","doi":"10.4310/ajm.2023.v27.n5.a1","DOIUrl":null,"url":null,"abstract":"Let $T_1, \\dotsc , T_m$ be a family of $d \\times d$ invertible real matrices with $\\rVert T_i \\rvert \\lt 1/2$ for $1 \\leq i \\leq m$. We provide some sufficient conditions on these matrices such that the self-affine set generated by the iterated function system $\\lbrace T_i x + a_i \\rbrace$ on $\\mathbb{R}^d$ has non-empty interior for almost all $(a_1 , \\dotsc , a_m) \\in \\mathbb{R}^{md}$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Typical self-affine sets with non-empty interior\",\"authors\":\"De-Jun Feng, Zhou Feng\",\"doi\":\"10.4310/ajm.2023.v27.n5.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $T_1, \\\\dotsc , T_m$ be a family of $d \\\\times d$ invertible real matrices with $\\\\rVert T_i \\\\rvert \\\\lt 1/2$ for $1 \\\\leq i \\\\leq m$. We provide some sufficient conditions on these matrices such that the self-affine set generated by the iterated function system $\\\\lbrace T_i x + a_i \\\\rbrace$ on $\\\\mathbb{R}^d$ has non-empty interior for almost all $(a_1 , \\\\dotsc , a_m) \\\\in \\\\mathbb{R}^{md}$.\",\"PeriodicalId\":55452,\"journal\":{\"name\":\"Asian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ajm.2023.v27.n5.a1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ajm.2023.v27.n5.a1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let $T_1, \dotsc , T_m$ be a family of $d \times d$ invertible real matrices with $\rVert T_i \rvert \lt 1/2$ for $1 \leq i \leq m$. We provide some sufficient conditions on these matrices such that the self-affine set generated by the iterated function system $\lbrace T_i x + a_i \rbrace$ on $\mathbb{R}^d$ has non-empty interior for almost all $(a_1 , \dotsc , a_m) \in \mathbb{R}^{md}$.