{"title":"Zaremba理论中Cantor集的严格维数估计","authors":"O. Jenkinson, M. Pollicott","doi":"10.1090/conm/744/14980","DOIUrl":null,"url":null,"abstract":"We address the question of the accuracy of bounds used in the study of Zaremba’s conjecture. Specifically, we establish rigorous estimates on the Hausdorff dimension of certain Cantor sets which arise in the analysis of Zaremba’s conjecture in [5, 18, 19, 23].","PeriodicalId":412693,"journal":{"name":"Dynamics: Topology and Numbers","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Rigorous dimension estimates for Cantor sets\\n arising in Zaremba theory\",\"authors\":\"O. Jenkinson, M. Pollicott\",\"doi\":\"10.1090/conm/744/14980\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We address the question of the accuracy of bounds used in the study of Zaremba’s conjecture. Specifically, we establish rigorous estimates on the Hausdorff dimension of certain Cantor sets which arise in the analysis of Zaremba’s conjecture in [5, 18, 19, 23].\",\"PeriodicalId\":412693,\"journal\":{\"name\":\"Dynamics: Topology and Numbers\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dynamics: Topology and Numbers\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/744/14980\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamics: Topology and Numbers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/744/14980","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Rigorous dimension estimates for Cantor sets
arising in Zaremba theory
We address the question of the accuracy of bounds used in the study of Zaremba’s conjecture. Specifically, we establish rigorous estimates on the Hausdorff dimension of certain Cantor sets which arise in the analysis of Zaremba’s conjecture in [5, 18, 19, 23].
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