{"title":"论小订单的可实现性","authors":"Ioannis Iakovoglou","doi":"10.4064/fm178-4-2022","DOIUrl":null,"url":null,"abstract":"In this paper we're considering the question of whether or not a partial order on a finite set is realisable as a Smale order of a structurally stable diffeomorphism or flow acting on a closed manifold. We classify the orders that are realisable by 1) an $\\Omega$-stable diffeomorphism acting on a closed surface 2) an Anosov flow on a closed 3-manifold 3) a stable diffeomorphism with trivial attractors and repellers acting on a closed surface.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the realisability of Smale orders\",\"authors\":\"Ioannis Iakovoglou\",\"doi\":\"10.4064/fm178-4-2022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we're considering the question of whether or not a partial order on a finite set is realisable as a Smale order of a structurally stable diffeomorphism or flow acting on a closed manifold. We classify the orders that are realisable by 1) an $\\\\Omega$-stable diffeomorphism acting on a closed surface 2) an Anosov flow on a closed 3-manifold 3) a stable diffeomorphism with trivial attractors and repellers acting on a closed surface.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/fm178-4-2022\",\"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/10.4064/fm178-4-2022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we're considering the question of whether or not a partial order on a finite set is realisable as a Smale order of a structurally stable diffeomorphism or flow acting on a closed manifold. We classify the orders that are realisable by 1) an $\Omega$-stable diffeomorphism acting on a closed surface 2) an Anosov flow on a closed 3-manifold 3) a stable diffeomorphism with trivial attractors and repellers acting on a closed surface.
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