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On shadowing: ordinary and ergodic. (English) Zbl 1293.37014
Summary: The aim of this paper is to introduce the notion of ergodic shadowing for a continuous onto map which is equivalent to the map being topologically mixing and has the ordinary shadowing property. In particular, we deduce the chaotic behavior of a map with ergodic shadowing property. Moreover, we define some kind of specification property and investigate its relation to the ergodic shadowing property.

MSC:
37B99 Topological dynamics
37A25 Ergodicity, mixing, rates of mixing
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
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