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Iterative properties on flow

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DOI: 10.23977/compag.2020.010101 | Downloads: 6 | Views: 1699

Author(s)

Zhongxuan Yang 1, Dongmei Shen 2

Affiliation(s)

1 School of science, East China Jiaotong University , Nanchang 330013
2 Nanchang Institute of Science and Technology, Nanchang 330108

Corresponding Author

Zhongxuan Yang

ABSTRACT

In this paper, we consider a continuous flow φ:R×X→X,where X is a compact metric space,and we prove that for any positive integer N, φ is distributional chaotic if and only if φ^N is distributional chaotic;φ is Li-Yorke chaotic if and only if φ^N is Li-Yorke chaotic. 

KEYWORDS

distributional chaos, continuous flow, Li-Yorke chaos

CITE THIS PAPER

Zhongxuan Yang, Dongmei Shen, Iterative properties on flow . Complex Analysis and Geometry (2020) Vol. 1: 1-6. DOI: http://dx.doi.org/10.23977/compag.2020.010101.

REFERENCES

[1]  Li. T. Y, Yorke. J. Period three implies chaos. Amer. Math. Mothly,1975, 82: 985–992. 
[2] Berthold. S, Jaroslav. S. Measures of chaos and a spectral decomposition of dynamical systems of the interval. Trans, Amer. Math. Soc, 1994, 344: 737-754. 
[3] Wang. L. D, Huan. S. M, Huang. G. F. A note on Schweizer - Smital chaos. Nonlinear. Anal. 2008, 68: 1682-1686. 
[4] Huang. Y, Zhou. Z. L. Two new recurrent levels for  -Flows. Acta. Appl. Math, 2012, 118: 125-145. 

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