English

A note on odometers and shadowing

Dynamical Systems 2025-02-12 v1

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.

Keywords

Cite

@article{arxiv.2502.07334,
  title  = {A note on odometers and shadowing},
  author = {Noriaki Kawaguchi},
  journal= {arXiv preprint arXiv:2502.07334},
  year   = {2025}
}

Comments

11 pages

R2 v1 2026-06-28T21:39:51.708Z