A note on odometers and shadowing

Noriaki Kawaguchi

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arXiv · 2502.07334

A note on odometers and shadowing

Noriaki Kawaguchi

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Abstract

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. 2025-02-11. A note on odometers and shadowing. https://arxiv.org/abs/2502.07334

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