  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.
