Ergodic properties of invariant measures for systems with average shadowing property

• DOI: 10.48550/arxiv.1312.0292
• Publication Date: 2013-01-01
• Authors: Yiwei Dong; Xueting Tian; Xiaoping Yuan
• Keywords: Orbit (dynamics)

In this paper, we explore a topological system $f:M\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact connected subset $V\subseteq\mathcal {M}_{inv}(f)$ coincides $V_f(y)$, where $\mathcal denotes the space of invariant Borel probability measures on M, $V_f(y)$ accumulation set time Dirac supported at orbit $y$. also $M_{V}=\{y\in M\,\,|\,\,V_{f}(y)=V\}$ is dense in $Δ_{V}=\bigcup_{ν\in V}supp(ν)$. particular, if $Δ_{max}=\bigcup_{ν\in\mathcal {M}_{inv}(f)}supp(ν)$ isolated or $M$, then $M_{max}=\{y: V_{f}(y)=\mathcal {M}_{inv}(f)\}$ residual $Δ_{max}$.