Shadowing maps
Dynamical Systems
2025-04-02 v1
Abstract
This article is about the shadowing property of homeomorphisms on compact metric spaces and the map associating a point of the space to each pseudo-orbit, called 'shadowing map'. Based on some particular dynamical properties, as expansivity, we develop a brief theory and a hierarchy of such maps. We consider examples as odometers, shifts on infinite spaces, topologically hyperbolic homeomorphisms and north-shouth dynamics. We revisit a well-known technique for proving shadowing of expansive homeomorphisms with canonical coordinates due to R. Bowen, to obtain a shadowing map with the property we call 'self-tuning' from a hyperbolic bracket. This notion is introduced as part of the hierarchy of shadowing maps studied in this paper.
Cite
@article{arxiv.2504.00171,
title = {Shadowing maps},
author = {Alfonso Artigue},
journal= {arXiv preprint arXiv:2504.00171},
year = {2025}
}