Mauro Artigiani, C. Fougeron, P. Hubert, A. Skripchenko
{"title":"A note on double rotations of infinite type","authors":"Mauro Artigiani, C. Fougeron, P. Hubert, A. Skripchenko","doi":"10.1090/mosc/311","DOIUrl":null,"url":null,"abstract":"We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than \n\n \n 3\n 3\n \n\n. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mosc/311","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 4
Abstract
We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than
3
3
. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
