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The average-shadowing property and strong ergodicity. (English) Zbl 1210.37016
Let \(f\) and \(g\) be discrete dynamical systems on compact metric spaces with the average shadowing property (ASP). The paper proves the following facts:
1. Density of minimal points of \(f\) implies its total strong ergodicity (i.e. strong ergodicity of \(f^k\) for every \(k\in\mathbb{N}_+\)).
2. The product \(f\times g\) is topologically transitive and has the ASP.
3. If \(f\) is nontrivial and distal then it can’t have the ASP.
4. The full shift map over finite alphabet has the ASP.

MSC:
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
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