Devaney's chaos implies distributional chaos in a sequence (Q1044493)

For continuous mappings \(f:X\to X\) on complete metric spaces \(X\) without isolated points the authors show the following: If \(f\) is transitive and has a periodic point, then \(f\) is distributionally chaotic in a sequence, i.e.\ it has an uncountable distributionally chaotic set. In particular, chaos in the sense of Devaney is stronger than distributional chaos in a sequence.