Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664051 | Acta Mathematica Scientia | 2012 | 7 Pages |
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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