The structure on invariant measures of C (1) generic diffeomorphisms

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	The structure on invariant measures of C (1) generic diffeomorphisms
其他题名	The Structure on Invariant Measures of C1 Generic Diffeomorphisms
	Sun Wen Xiang 1; Tian Xue Ting 2
	2012
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	28 期号:4 页码:817-824
摘要	Let I > be an isolated non-trivial transitive set of a C (1) generic diffeomorphism f a Diff(M). We show that the space of invariant measures supported on I > coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in I > (which implies that the set of irregular(+) points is also residual in I >). As an application, we show that the non-uniform hyperbolicity of irregular(+) points in I > with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in I >) determines the uniform hyperbolicity of I >.
其他摘要	Let Λ be an isolated non-trivial transitive set of a C~1 generic diffeomorphism f ∈ Diff(M). We show that the space of invariant measures supported on Λ 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 Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ.
关键词	UNIFORM HYPERBOLICITY Generic property invariant measure and periodic measure hyperbolic basic set topologically transitive irregular point
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation] ; [CAPES (Brazil)]
CSCD记录号	CSCD:4510401
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/53008
专题	中国科学院数学与系统科学研究院
作者单位	1.北京大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Sun Wen Xiang,Tian Xue Ting. The structure on invariant measures of C (1) generic diffeomorphisms[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2012,28(4):817-824.
APA	Sun Wen Xiang,&Tian Xue Ting.(2012).The structure on invariant measures of C (1) generic diffeomorphisms.ACTA MATHEMATICA SINICA-ENGLISH SERIES,28(4),817-824.
MLA	Sun Wen Xiang,et al."The structure on invariant measures of C (1) generic diffeomorphisms".ACTA MATHEMATICA SINICA-ENGLISH SERIES 28.4(2012):817-824.