| Title | Ergodic properties of invariant measures for C1+alpha non-uniformly hyperbolic systems |
| Authors | Liang, Chao Sun, Wenxiang Tian, Xueting |
| Affiliation | Cent Univ Finance & Econ, Dept Appl Math, Beijing 100081, Peoples R China. Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China. Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China. Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China. |
| Issue Date | 2013 |
| Publisher | ergodic theory and dynamical systems |
| Citation | ERGODIC THEORY AND DYNAMICAL SYSTEMS.2013,33,560-584. |
| Abstract | For every ergodic hyperbolic measure omega of a C1+alpha diffeomorphism, there is an ! -full-measure set (Lambda) over tilde (the union of (Lambda) over tilde (l) = supp(omega vertical bar Lambda(l)) the support sets of omega on each Pesin block Lambda(l), l = 1, 2, ...) such that every non-empty, compact and connected subset V subset of Closure (M-inv ((Lambda) over tilde)) coincides with V-f(x), where M-inv((Lambda) over tilde) denotes the space of invariant measures supported on (Lambda) over tilde and V-f(x) denotes the accumulation set of time averages of Dirac measures supported at one orbit of some point x. For each fixed set V, the points with the above property are dense in the support supp(omega). In particular, points satisfying V-f(x) = Closure (M-inv ((Lambda) over tilde)) are dense in supp(omega). Moreover, if supp (omega) is isolated, the points satisfying V-f(x) superset of Closure (M-inv((Lambda) over tilde)) form a residual subset of supp (omega). These extend results of K. Sigmund [On dynamical systems with the specification property. Trans. Amer. Math. Soc. 190 (1974), 285-299] (see also M. Denker, C. Grillenberger and K. Sigmund [Ergodic Theory on Compact Spaces (Lecture Notes in Mathematics, 527). Springer, Berlin, Ch. 21]) from the uniformly hyperbolic case to the non-uniformly hyperbolic case. As a corollary, irregular(+) points form a residual set of supp(omega). |
| URI | http://hdl.handle.net/20.500.11897/391844 |
| ISSN | 0143-3857 |
| Indexed | SCI(E) |
| Appears in Collections: | 数学科学学院 数学及其应用教育部重点实验室 |
