S-limit shadowing implies the denseness of chain components with the shadowing property
Dynamical Systems
2023-07-31 v1
Abstract
For any continuous self-map of a compact metric space, we consider the space of chain components and prove that the s-limit shadowing implies the denseness of chain components with the shadowing property. It gives a partial answer to a question raised by Moothathu [Topology Appl. 158 (2011) 2232--2239]. We also prove that the s-limit shadowing is not generic in the space of homeomorphisms of a closed differentiable manifold.
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Cite
@article{arxiv.2307.15303,
title = {S-limit shadowing implies the denseness of chain components with the shadowing property},
author = {Noriaki Kawaguchi},
journal= {arXiv preprint arXiv:2307.15303},
year = {2023}
}
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8 pages