{"title":"ℤd-作用的准阴影","authors":"Juan Pan, Xian Kun Ren, Yun Hua Zhou","doi":"10.1007/s10114-023-1681-1","DOIUrl":null,"url":null,"abstract":"<div><p>A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent. We prove that a <i>C</i><sup>1</sup>-smooth ℤ<sup><i>d</i></sup>-action has the quasi-shadowing property if one of the generators is <i>C</i><sup>1+<i>α</i></sup> (<i>α</i> > 0) non-uniformly partially hyperbolic.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-shadowing for ℤd-actions\",\"authors\":\"Juan Pan, Xian Kun Ren, Yun Hua Zhou\",\"doi\":\"10.1007/s10114-023-1681-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent. We prove that a <i>C</i><sup>1</sup>-smooth ℤ<sup><i>d</i></sup>-action has the quasi-shadowing property if one of the generators is <i>C</i><sup>1+<i>α</i></sup> (<i>α</i> > 0) non-uniformly partially hyperbolic.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-023-1681-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-1681-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent. We prove that a C1-smooth ℤd-action has the quasi-shadowing property if one of the generators is C1+α (α > 0) non-uniformly partially hyperbolic.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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