The asymptotic average shadowing property and strong ergodicity

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• 作者：Yingxuan Niu^a ; ^{yxniu@wxc.edu.cn} ; Yi Wang^a ; ^{ewang@wxc.edu.cn} ; Shoubao Su^b ; ^{sooshoubo@wxc.edu.cn}
• 刊名：Chaos, Solitons and Fractals
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：53
• 期：Complete
• 页码：34-38
• 全文大小：344 K

文摘

Let X be a compact metric space and f : X ¡ú 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 ? 1, f ¡Á f ¡Á ? ¡Á f(n times) and fⁿ are totally strongly ergodic. Moreover, we also give some sufficient conditions for an interval map having the AASP to be Li-Yorke chaotic.