{"title":"一般微分同态的链传递集上的轨道阴影性质","authors":"Manseob Lee","doi":"10.2478/ausm-2020-0009","DOIUrl":null,"url":null,"abstract":"Abstract Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":"38 1","pages":"146 - 154"},"PeriodicalIF":0.6000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Orbital shadowing property on chain transitive sets for generic diffeomorphisms\",\"authors\":\"Manseob Lee\",\"doi\":\"10.2478/ausm-2020-0009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.\",\"PeriodicalId\":43054,\"journal\":{\"name\":\"Acta Universitatis Sapientiae-Mathematica\",\"volume\":\"38 1\",\"pages\":\"146 - 154\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Universitatis Sapientiae-Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/ausm-2020-0009\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Universitatis Sapientiae-Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/ausm-2020-0009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Orbital shadowing property on chain transitive sets for generic diffeomorphisms
Abstract Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.
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