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 acting on a compact metric space , 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}
}