an:06578178
Zbl 1339.37003
Niu, Yingxuan; Wang, Yi; Su, Shoubao
The asymptotic average shadowing property and strong ergodicity
EN
Chaos Solitons Fractals 53, 34-38 (2013).
00355265
2013
j
37A25 37C50 37D45
Summary: Let \(X\) be a compact metric space and \(f:X\to X\) be a continuous map. In this paper, we prove that if \(f\) has the asymptotic average shadowing property (Abbrev. AASP) and an invariant Borel probability measure with full support or the positive upper Banach density recurrent points of \(f\) are dense in \(X\), then for all \(n\geqslant 1,f\times f\times\cdots\times f\) (\(n\) times) and \(f^n\) are totally strongly ergodic. Moreover, we also give some sufficient conditions for an interval map having the AASP to be Li-Yorke chaotic.