{"title":"具有遍历导数扩张的光滑零熵微分同胚","authors":"Philipp Kunde","doi":"10.4171/cmh/478","DOIUrl":null,"url":null,"abstract":"On any smooth compact and connected manifold of dimension 2 admitting a smooth nontrivial circle action we construct C∞-diffeomorphisms of topological entropy zero whose differential is ergodic with respect to a smooth measure in the projectivization of the tangent bundle. The proof is based on a version of the “approximation by conjugation”-method.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/478","citationCount":"1","resultStr":"{\"title\":\"Smooth zero-entropy diffeomorphisms with ergodic derivative extension\",\"authors\":\"Philipp Kunde\",\"doi\":\"10.4171/cmh/478\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"On any smooth compact and connected manifold of dimension 2 admitting a smooth nontrivial circle action we construct C∞-diffeomorphisms of topological entropy zero whose differential is ergodic with respect to a smooth measure in the projectivization of the tangent bundle. The proof is based on a version of the “approximation by conjugation”-method.\",\"PeriodicalId\":50664,\"journal\":{\"name\":\"Commentarii Mathematici Helvetici\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2020-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/cmh/478\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Commentarii Mathematici Helvetici\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/cmh/478\",\"RegionNum\":3,\"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":"Commentarii Mathematici Helvetici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/cmh/478","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Smooth zero-entropy diffeomorphisms with ergodic derivative extension
On any smooth compact and connected manifold of dimension 2 admitting a smooth nontrivial circle action we construct C∞-diffeomorphisms of topological entropy zero whose differential is ergodic with respect to a smooth measure in the projectivization of the tangent bundle. The proof is based on a version of the “approximation by conjugation”-method.
期刊介绍：
Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals.
Commentarii Mathematici Helvetici is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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