FURTHER DISCUSSION ON KATO’S CHAOS IN SET-VALUED DISCRETE SYSTEMS

For a compact metric space Y and a continuous map g: Y → Y, the collective accessibility and collectively Kato chaotic of the dynamical system (Y, g) were defined. The relations between topologically weakly mixing and collective accessibility, or strong accessibility, or strongly Kato chaos were studied. Some common properties of g and g were given. Where g: κ(Y) → κ(Y) is defined as g(B) = g(B) for any B ∈ κ(Y), and κ(Y) is the collection of all nonempty compact subsets of Y. Moreover, it is proved that g is collectively accessible (or strongly accessible) if and only if g in w^e-topology is collectively accessible (or strongly accessible).