The average-shadowing property and strong ergodicity |
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Authors: | Yingxuan Niu |
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Affiliation: | Department of Mathematics and Physics, West Anhui University, Lu'an, Anhui 237012, PR China |
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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 average-shadowing property and the minimal points of f are dense in X, then f is weakly mixing and totally strongly ergodic. As applications we obtain that if f is a distal or Lyapunov stable map having the average-shadowing property, then X is consisting of one point. Moreover, we illustrate that the full shift has the average-shadowing property. |
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Keywords: | The average-shadowing property Topologically ergodic Strongly ergodic Totally strongly ergodic Minimal point Distal Lyapunov stable |
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