{"title":"Sierpinski地毯的<s:2>拓扑共形维数","authors":"A. Mabrouk, Z. Douzi, B. Selmi","doi":"10.1080/1726037X.2022.2079264","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"33 - 53"},"PeriodicalIF":0.4000,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The ϕ-Topological Conformal Dimension for the Sierpinski Carpet\",\"authors\":\"A. Mabrouk, Z. Douzi, B. Selmi\",\"doi\":\"10.1080/1726037X.2022.2079264\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.\",\"PeriodicalId\":42788,\"journal\":{\"name\":\"Journal of Dynamical Systems and Geometric Theories\",\"volume\":\"20 1\",\"pages\":\"33 - 53\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamical Systems and Geometric Theories\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1726037X.2022.2079264\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2022.2079264","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The ϕ-Topological Conformal Dimension for the Sierpinski Carpet
Abstract In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.
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