Li-Yorke sensitivity of set-valued discrete systems
type: Item
instance of: scholarly article
title: Li-Yorke sensitivity of set-valued discrete systems
zbMATH Open document ID: 1397.54045
DOI: 10.1155/2013/260856
author: Heng Liu
author: Lidong Wang
author: Fengchun Lei
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: Consider the surjective, continuous map \(f:X\to X\) and the continuous map \(\overline f\) of \(\mathcal K(X)\) induced by \(f\), where \(X\) is a compact metric space and \(\mathcal K(X)\) is the space of all nonempty compact subsets of \(X\) endowed with the Hausdorff metric. In this paper, we give a short proof that if \(\overline f\) is Li-Yoke sensitive, then \(f\) is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of \(f\) does not imply Li-Yorke sensitivity of \(\overline f\).
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 6950588
Wikidata QID: Q59002432
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/260856
OpenAlex ID: W2161591237
DBLP publication ID: journals/jam/LiuLW13
description: scientific article; zbMATH DE number 6950588