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arXiv · 2011.13128

A new version of distributional chaos and the relations between distributional chaos in a sequence and other concepts of chaos

H. B. Zeng
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Abstract

In this paper we consider relations between distributional chaos in a sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We give a sufficient condition and prove that the distributional chaos is equivalent to the distributional chaos in a sequence under this condition. Besides, we get that distributional chaos in a sequence and w-chaos(R-T chaos, DC 3, respectively)do not imply each other. Finally, we give a new definition of chaos, named DC 2', which is similar to DC 2, and show that for any integer N > 0, f is DC 2' if and only if f^N is also DC 2'.

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H. B. Zeng. 2020-11-26. A new version of distributional chaos and the relations between distributional chaos in a sequence and other concepts of chaos. https://arxiv.org/abs/2011.13128

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