{"title":"Dynamical coherence in isotopy classes of fibered lifted partially hyperbolic diffeomorphisms","authors":"Luis Pedro Piñeyrúa, Martín Sambarino","doi":"10.1007/s00209-024-03535-3","DOIUrl":null,"url":null,"abstract":"<p>We introduce the notion of <i>fibered lifted partially hyperbolic diffeomorphisms</i> and we prove that any partially hyperbolic diffeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic systems is dynamically coherent. Moreover we prove some global stability result: every two partially hyperbolic diffeomorphisms in the same connected component of a fibered lifted partially hyperbolic diffeomorphisms are leaf conjugate.\n</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"67 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03535-3","RegionNum":3,"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
We introduce the notion of fibered lifted partially hyperbolic diffeomorphisms and we prove that any partially hyperbolic diffeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic systems is dynamically coherent. Moreover we prove some global stability result: every two partially hyperbolic diffeomorphisms in the same connected component of a fibered lifted partially hyperbolic diffeomorphisms are leaf conjugate.
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