A+ CATEGORY SCIENTIFIC UNIT

A note on odometers and shadowing

Noriaki Kawaguchi Colloquium Mathematicum 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.

Authors

  • Noriaki KawaguchiDepartment of Mathematical and Computing Science
    School of Computing
    Institute of Science Tokyo
    152-8552 Tokyo, Japan
    e-mail

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