Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps

Several chaotic properties of cyclic permutation maps are considered. Cyclic permutation maps refer to p-dimensional dynamical systems of the form phi (b(1), b(2), . . . , b(p)) = (u(p)(b(p)), u(1)(b(1)), . . . , u(p-1)(b(p-1))), where b(j) is an element of H-j (j is an element of {1,2, . . . , p}), p >= 2 is an integer, and H-j (j is an element of {1, 2, . . . , p}) are compact subintervals of the real line R = (-infinity, +infinity ). u(j) : H-j -> Hj+1(j = 1, 2, ... , p - 1) and u(p) : H-p -> H-1 are continuous maps. Necessary and sufficient conditions for a class of cyclic permutation maps to have Li-Yorke chaos, distributional chaos in a sequence, distributional chaos, or Li-Yorke sensitivity are given. These results extend the existing ones.