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 ave...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.展开更多
基金supported by National Natural Science Foundation(Grant Nos.10671006,10831003)supported by CAPES(Brazil)
文摘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.