The structure on invariant measures of C1 generic diffeomorphisms |
| |
| Authors: | Wen Xiang Sun Xue Ting Tian |
| |
| Affiliation: | (1) LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China;(2) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China;(3) School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China |
| |
| Abstract: | 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. |
| |
| Keywords: | Generic property invariant measure and periodic measure hyperbolic basic set topolog-ically transitive irregular point |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ |
|
