On the completely irregular set for systems with the shadowing property
Dynamical Systems
2023-07-20 v2
Abstract
We prove that the completely irregular set is Baire generic for every non-uniquely ergodic transitive continuous map which satisfies the shadowing property and acts on a compact metric space without isolated points. We also show that, under the previous assumptions, the orbit of any completely irregular point is dense. Afterwards, we analyze the connection between transitivity and the shadowing property, draw a few consequences of their joint action within the family of expansive homeomorphisms, and discuss several examples to test the scope of our results.
Cite
@article{arxiv.2307.02562,
title = {On the completely irregular set for systems with the shadowing property},
author = {Maria Carvalho and Vinícius Coelho and Luciana Salgado},
journal= {arXiv preprint arXiv:2307.02562},
year = {2023}
}
Comments
32 pages, no figures, Changes in Abstract and distribution of sections