In this paper, we study some chaotic properties ofs-dimensional dynamical system of the formΨa1,a2,…,as=gsas,g1a1,…,gs−1as−1,whereak∈Hkfor anyk∈1,2,…,s, s≥2is an integer, andHkis a compact subinterval of the real lineℝ=−∞,+∞for anyk∈1,2,…,s. Particularly, a necessary and sufficient condition for a cyclic permutation mapΨa1,a2,…,as=gsas,g1a1,…,gs−1as−1to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropyhΨof such a cyclic permutation map is the same as the topological entropy of each of the following maps:gj∘gj−1∘⋯∘g1l∘gs∘gs−1∘⋯∘gj+1,ifj=1,…,s−1andgs∘gs−1∘⋯∘g1, and thatΨis sensitive if and only if at least one of the coordinates maps ofΨsis sensitive.