Acta mathematica scientia, Series B >
DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES
Received date: 2009-08-05
Revised date: 2011-02-27
Online published: 2012-03-20
Supported by
Tian is the corresponding author and supported by CAPES(Brazil); Sun is supported by National Natural Science Foundation (10671006, 10831003) and National Basic Research Program of China (973 Program) (2006CB805903).
Let M be a smooth compact manifold and ∧ be a compact invariant set. In this article, we prove that, for every robustly transitive set ∧, f|∧ satisfies a C1-generic-stable shadowable property (resp., C1-generic-stable transitive specification property or C1-generic-stable barycenter property) if and only if ∧ is a hyperbolic basic set. In partic-ular, f|∧ satisfies a C1-stable shadowable property (resp., C1-stable transitive specification property or C1-stable barycenter property) if and only if ∧ is a hyperbolic basic set. Similar results are valid for volume-preserving case.
TIAN Xue-Ting , SUN Wen-Xiang . DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 552 -558 . DOI: 10.1016/S0252-9602(12)60037-X
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