{"title":"Non-rigidity of partially hyperbolic abelian -actions on tori","authors":"FEDERICO RODRIGUEZ HERTZ, ZHIREN WANG","doi":"10.1017/etds.2024.18","DOIUrl":null,"url":null,"abstract":"We prove that every genuinely partially hyperbolic <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline2.png\"/> <jats:tex-math> $\\mathbb {Z}^r$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-action by toral automorphisms can be perturbed in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline3.png\"/> <jats:tex-math> $C^1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-topology, so that the resulting action is continuously conjugate, but not <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline4.png\"/> <jats:tex-math> $C^1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-conjugate, to the original one.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"42 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ergodic Theory and Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/etds.2024.18","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that every genuinely partially hyperbolic $\mathbb {Z}^r$ -action by toral automorphisms can be perturbed in $C^1$ -topology, so that the resulting action is continuously conjugate, but not $C^1$ -conjugate, to the original one.
期刊介绍：
Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.
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