Dmitry Dolgopyat, Adam Kanigowski, Federico Rodriguez Hertz
{"title":"Exponential mixing implies Bernoulli | Annals of Mathematics","authors":"Dmitry Dolgopyat, Adam Kanigowski, Federico Rodriguez Hertz","doi":"10.4007/annals.2024.199.3.5","DOIUrl":null,"url":null,"abstract":"<p>Let $f$ be a $C^{1+\\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\\mu$. We show that if $f\\colon (M,\\mu)\\to (M,\\mu)$ is exponentially mixing, then it is Bernoulli.</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":5.7000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4007/annals.2024.199.3.5","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f\colon (M,\mu)\to (M,\mu)$ is exponentially mixing, then it is Bernoulli.
期刊介绍：
The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.
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