Scrambled and distributionally scrambled n-tuples

@inproceedings{Dolevzelova2013ScrambledAD,
  title={Scrambled and distributionally scrambled n-tuples},
  author={Jana Dolevzelov'a},
  year={2013}
}
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.