{"title":"由吸引子的均匀分岔和零密度产生的非均匀双曲马蹄铁","authors":"Jacob Palis , Jean-Christophe Yoccoz","doi":"10.1016/S0764-4442(01)02139-5","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>f</em><sub>0</sub> be a surface diffeomorphism such that the maximal invariant set in an open set <em>V</em> is the union of a horseshoe and a quadratic tangency between the stable and unstable foliations of this horseshoe. We assume that the dimension of the horseshoe is larger than but close to one. We announce that, for most diffeomorphisms <em>f</em> close to <em>f</em><sub>0</sub>, the maximal <em>f</em>-invariant set in <em>V</em> is a non-uniformly hyperbolic horseshoe, with dynamics of the same type as met in Hénon attractors.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 867-871"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02139-5","citationCount":"18","resultStr":"{\"title\":\"Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs\",\"authors\":\"Jacob Palis , Jean-Christophe Yoccoz\",\"doi\":\"10.1016/S0764-4442(01)02139-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>f</em><sub>0</sub> be a surface diffeomorphism such that the maximal invariant set in an open set <em>V</em> is the union of a horseshoe and a quadratic tangency between the stable and unstable foliations of this horseshoe. We assume that the dimension of the horseshoe is larger than but close to one. We announce that, for most diffeomorphisms <em>f</em> close to <em>f</em><sub>0</sub>, the maximal <em>f</em>-invariant set in <em>V</em> is a non-uniformly hyperbolic horseshoe, with dynamics of the same type as met in Hénon attractors.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 9\",\"pages\":\"Pages 867-871\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02139-5\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021395\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021395","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs
Let f0 be a surface diffeomorphism such that the maximal invariant set in an open set V is the union of a horseshoe and a quadratic tangency between the stable and unstable foliations of this horseshoe. We assume that the dimension of the horseshoe is larger than but close to one. We announce that, for most diffeomorphisms f close to f0, the maximal f-invariant set in V is a non-uniformly hyperbolic horseshoe, with dynamics of the same type as met in Hénon attractors.
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