Shadowing maps

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Artigue, Alfonso
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908292433838080
author Artigue, Alfonso
author_facet Artigue, Alfonso
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00171
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Shadowing maps
Artigue, Alfonso
Dynamical Systems
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.
title Shadowing maps
topic Dynamical Systems
url https://arxiv.org/abs/2504.00171