{"title":"余维一特殊的Anosov自同态","authors":"Xiang Zhang","doi":"10.1080/14689367.2022.2164708","DOIUrl":null,"url":null,"abstract":"We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On codimension one special Anosov endomorphisms\",\"authors\":\"Xiang Zhang\",\"doi\":\"10.1080/14689367.2022.2164708\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.\",\"PeriodicalId\":50564,\"journal\":{\"name\":\"Dynamical Systems-An International Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-02-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dynamical Systems-An International Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/14689367.2022.2164708\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2022.2164708","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
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