{"title":"环上部分双曲阿贝尔作用的非刚性","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/etds.2024.18\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/etds.2024.18","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-rigidity of partially hyperbolic abelian -actions on tori
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.
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