{"title":"无穷保角迭代函数系统的维谱","authors":"Tushar Das, David Simmons","doi":"10.4171/JFG/112","DOIUrl":null,"url":null,"abstract":"The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba\\'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2019-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the dimension spectra of infinite conformal iterated function systems\",\"authors\":\"Tushar Das, David Simmons\",\"doi\":\"10.4171/JFG/112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba\\\\'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2019-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/JFG/112\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fractal Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JFG/112","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the dimension spectra of infinite conformal iterated function systems
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba\'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.
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