The asymptotic average shadowing property and strong ergodicity

Yingxuan Niu, Yi Wang and Shoubao Su

Chaos, Solitons & Fractals, 2013, vol. 53, issue C, 34-38

Abstract: Let X be a compact metric space and f:X→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×f×⋯×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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:53:y:2013:i:c:p:34-38

DOI: 10.1016/j.chaos.2013.04.009

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