Scrambled and distributionally scrambled n-tuples

Abstract

This article investigates the relation between the distributional chaos and the existence of a scrambled triple. We show that for a continuous mapping $f$ acting on a compact metric space $(X,d)$, the possession of an infinite extremal distributionally scrambled set is not sufficient for the existence of a scrambled triple. We also construct an invariant Mycielski set with an uncountable extremal distributionally scrambled set without any scrambled triple.

References in corpus (2)

• Chaos and Entropy for Interval Maps
• On $n$-scrambled tuples and distributional chaos in a sequence