Devaney Chaos on a Set-valued Map and Its Inverse Limit
arXiv:2210.13719 · doi:10.1016/j.chaos.2023.113454
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.