DC3 and Li–Yorke chaos

Wang, Hui; Lei, Fengchun; Wang, Lidong

doi:10.1016/j.aml.2014.01.004

Cited by 7 publications

(2 citation statements)

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“…In the following example, we will show that DC2' is also neither equivalent to DC1 nor DC2. DC2' is not equivalent to DC3 by (c) and [13]. So the four versions of distributional chaos(DC1,DC2,DC2',DC3) are mutually nonequivalent.…”

Section: Preliminaries and Definitionsmentioning

confidence: 97%

“…Since then, surely, it is an important question to understand the relation among the various definitions. And there are many results about that [6,[8][9][10][11][12][13][14][15][16][17][18][19]. In order to reveal the links between distributional chaos and chaos in the sense of Li and Yorke, the concept of distributional chaos in a sequence was introduced in [7].…”

Section: Introductionmentioning

confidence: 99%

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A New Version of Distributional Chaos, Distributional Chaos in a Sequence, and Other Concepts of Chaos

Zeng

2022

Int. J. Bifurcation Chaos

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In this paper, we investigate the relations between distributional chaos in a sequence and distributional chaos ([Formula: see text]-chaos, R–T chaos, DC3, respectively). Firstly, we prove a sufficient condition that the distributional chaos is equivalent to the distributional chaos in a sequence. Besides, we prove that distributional chaos in a sequence and [Formula: see text]-chaos (R–T chaos, DC3, respectively) do not imply each other. Finally, we give a new definition of chaos, named DC2[Formula: see text], which is similar to DC2, and show that DC2[Formula: see text] is an invariant of topological conjugacy and an iteration invariant (that is, for any integer [Formula: see text], [Formula: see text] is DC2[Formula: see text] if and only if [Formula: see text] is DC2[Formula: see text]).

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Section: Preliminaries and Definitionsmentioning

confidence: 97%