English

Scrambled and distributionally scrambled n-tuples

Dynamical Systems 2013-11-20 v1

Abstract

This article investigates the relation between the distributional chaos and the existence of a scrambled triple. We show that for a continuous mapping ff acting on a compact metric space (X,d)(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.

Cite

@article{arxiv.1311.4734,
  title  = {Scrambled and distributionally scrambled n-tuples},
  author = {Jana Doleželová},
  journal= {arXiv preprint arXiv:1311.4734},
  year   = {2013}
}
R2 v1 2026-06-22T02:10:26.242Z