A note on odometers and shadowing
Volume 179 / 2025
Colloquium Mathematicum 179 (2025), 21-34
MSC: Primary 37B20; Secondary 37B65
DOI: 10.4064/cm9634-7-2025
Published online: 7 August 2025
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.
