Analysis shows that shadowing property ensures dense periodic orbits in compact metric spaces.
For a continuous self-map of a compact metric space, we provide a sufficient condition for the orbit of a point to converge to a periodic orbit or an odometer. We show that if a continuous self-map of a compact metric space has the shadowing property, then the set of points whose orbits converge to periodic orbits or odometers is dense.
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Noriaki Kawaguchi (2025) studied this question.
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