DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES |
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Authors: | Tian Xueting Sun Wenxiang |
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Institution: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China Departamento de Matemática, Universidade Federal de Alagoas, Maceió 57072-090, Brazil 2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China |
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Abstract: | Let M be a smooth compact manifold and Λ be a compact invariant set. In this article, we prove that, for every robustly transitive set Λ, f|∧ satisfies a C1-genericstable shadowable property (resp., C1-generic-stable transitive specification property or C1-generic-stable barycenter property) if and only if Λ is a hyperbolic basic set. In particular, f|∧ satisfies a C1-stable shadowable property (resp., C1-stable transitive specification property or C1-stable barycenter property) if and only if Λ is a hyperbolic basic set. Similar results are valid for volume-preserving case. |
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Keywords: | Specification property hyperbolic basic set topologically transitive shad-owing property |
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