THE EQUIVALENCE RELATIONSHIP BETWEEN LI-YORKE Δ-CHAOS AND DISTRIBUTIONAL Δ-CHAOS IN A SEQUENCE

The relationship between Li-Yorke chaos and distributional chaos in a sequence is discussed. It is pointed out that the set of distributional $\delta$-scramble pairs in a sequence $Q$ is a $G_\delta$ set, and Li-Yorke $\delta$-chaos is equivalent to distributional $\delta$-chaos in a sequence. A uniformly chaotic set is a distributional scramble set in some sequence and a class of transitive system implies distributional chaos in a sequence.