1. The average-shadowing property and strong ergodicity
- Author
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Niu, Yingxuan
- Subjects
- *
ERGODIC theory , *METRIC spaces , *SHADOWING theorem (Mathematics) , *COMPACT spaces (Topology) , *MATHEMATICAL mappings , *LYAPUNOV stability , *MAXIMA & minima - Abstract
Abstract: Let X be a compact metric space and 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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