Devaney Chaos on a Set-valued Map and Its Inverse Limit
Dynamical Systems
2023-05-31 v1
Abstract
We study relationships between a set-valued map and its inverse limits about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. Density of periodic point set of a set-valued map and its inverse limits implies each other. Sensitivity of a set-valued map and its inverse limits does not imply each other. Transitivity and Devaney chaos of generalized inverse limits implies the corresponding property of a set-valued map.
Cite
@article{arxiv.2210.13719,
title = {Devaney Chaos on a Set-valued Map and Its Inverse Limit},
author = {Yingcui Zhao and Lidong Wang and Nan Wang},
journal= {arXiv preprint arXiv:2210.13719},
year = {2023}
}