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.


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