The Structure on Invariant Measures of C^1 Generic Diffeomorphisms  

作　　者：Wen Xiang SUN Xue Ting TIAN 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences [3]School of Mathematical Sciences,Peking University

出　　处：《Acta Mathematica Sinica,English Series》2012年第4期817-824,共8页数学学报（英文版）

基　　金：supported by National Natural Science Foundation(Grant Nos.10671006,10831003);supported by CAPES(Brazil)

摘　　要：Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ （which implies that the set of irregular＋ points is also residual in Λ）. As an application, we show that the non-uniform hyperbolicity of irregular＋ points in A with totally 0 measure （resp., the non-uniform hyperbolicity of a generic subset in Λ） determines the uniform hyperbolicity of Λ.Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ （which implies that the set of irregular＋ points is also residual in Λ）. As an application, we show that the non-uniform hyperbolicity of irregular＋ points in A with totally 0 measure （resp., the non-uniform hyperbolicity of a generic subset in Λ） determines the uniform hyperbolicity of Λ.

关 键 词：Generic property invariant measure and periodic measure hyperbolic basic set topolog-ically transitive irregular point 

分 类 号：O189[理学—数学]