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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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##### References:
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