{"title":"论不变叶形的规律性","authors":"Dmitry Turaev","doi":"10.1134/S1560354724010027","DOIUrl":null,"url":null,"abstract":"<div><p>We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a <span>\\(C^{\\beta}\\)</span> map with <span>\\(\\beta>1\\)</span> is <span>\\(C^{1+\\varepsilon}\\)</span> with some <span>\\(\\varepsilon>0\\)</span>. The result is applied to the restriction of higher regularity\nmaps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Turaev)","pages":"6 - 24"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Regularity of Invariant Foliations\",\"authors\":\"Dmitry Turaev\",\"doi\":\"10.1134/S1560354724010027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a <span>\\\\(C^{\\\\beta}\\\\)</span> map with <span>\\\\(\\\\beta>1\\\\)</span> is <span>\\\\(C^{1+\\\\varepsilon}\\\\)</span> with some <span>\\\\(\\\\varepsilon>0\\\\)</span>. The result is applied to the restriction of higher regularity\\nmaps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"29 and Dmitry Turaev)\",\"pages\":\"6 - 24\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354724010027\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724010027","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a \(C^{\beta}\) map with \(\beta>1\) is \(C^{1+\varepsilon}\) with some \(\varepsilon>0\). The result is applied to the restriction of higher regularity
maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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