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arXiv · 1311.4734

Scrambled and distributionally scrambled n-tuples

Jana Doleželová
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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.

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Jana Doleželová. 2013-11-19. Scrambled and distributionally scrambled n-tuples. https://arxiv.org/abs/1311.4734

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