2016/08/22 by Mlíchová, Michaela, Štefánková, Marta
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1608.06269
A continuous map f on a compact metric space X induces in a natural way the map f on the hyperspace \mathcal K(X) of all closed non-empty subsets of X. We study the question of transmission of chaos between f and f. We deal with generic, generic ε-, dense and dense ε-chaos for interval maps. We prove that all four types of chaos transmit from f to f, while the converse transmission from f to f is true for generic, generic ε- and dense ε-chaos. Moreover, the transmission of dense ε- and generic ε-chaos from f to f is true for maps on general compact metric spaces.