Devaney’s chaos implies distributional chaos in a sequence Original Research Article

Let XX be a complete metric space without isolated points, and let f:X→Xf:X→X be a continuous map. In this paper we prove that if ff is transitive and has a periodic point of period pp, then ff is distributionally chaotic in a sequence. Particularly, chaos in the sense of Devaney is stronger than distributional chaos in a sequence.