Abstract
A continuous map f on a compact metric space X induces in a natural way the map on the hyperspace of all closed non-empty subsets of X. We study the question of transmission of chaos between f and . We deal with generic, generic -, dense and dense -chaos for interval maps. We prove that all four types of chaos transmit from f to , while the converse transmission from to f is true for generic, generic - and dense -chaos. Moreover, the transmission of dense - and generic -chaos from to f is true for maps on general compact metric spaces.
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