Mathematics – Dynamical Systems
Scientific paper
2010-11-24
Ergod. Th. & Dynam. Sys. 2012
Mathematics
Dynamical Systems
19 pages
Scientific paper
10.1017/S0143385711000940
For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$ diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tilde\Lambda)$ coincides with the accumulating set of time averages of Dirac measures supported at {\it one orbit}, where $\mathbb{M}_{inv}(\tilde\Lambda)$ denotes the space of invariant measures supported on $\tilde\Lambda$. Such state points corresponding to a fixed $V$ are dense in the support $supp(\omega)$. Moreover, $\mathbb{M}_{inv}(\tilde\Lambda)$ can be accumulated by time averages of Dirac measures supported at {\it one orbit}, and such state points form a residual subset of $supp(\omega)$. These extend results of Sigmund [9] from uniformly hyperbolic case to non-uniformly hyperbolic case. As a corollary, irregular points form a residual set of $supp(\omega)$.
Liang Chao
Sun Wenxiang
Tian Xueting
No associations
LandOfFree
Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-240483