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Reiterative Distributional Chaos in Non-autonomous Discrete Systems

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Abstract

In this paper, several types of reiterative distributional chaos are concerned in discrete dynamical systems. Some implications between distributional chaos and reiterative distributional chaos are obtained. It is further shown that an equicontinuous non-autonomous system \((X, f_{1, \infty })\), where \(f_{1, \infty } = \{f_i\}_{i \ge 1}\) is a sequence of self-maps of a metric space X, exhibits reiterative distributional chaos of type i (\(i \in \{1, 1^{+}, 2, 2\frac{1}{2}, 2\frac{1}{2}-\}\)) if and only if its kth iteration \(f^{[k]}_{1, \infty }\) exhibits reiterative distributional chaos of type i for any \(k \ge 2\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11801096, 11901091), Natural Science Foundation of Guangdong Province (No. 2020A1515010339), Natural Science Research Project of Guangdong Province (No. 2017KQNCX122), the Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications (No. 18TD0013) and Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems (No. 2017CXTD02). The authors would like to express their gratitude to the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China

    Zongbin Yin

  2. School of Mathematics and Big Data, Foshan University, Foshan, 528000, People’s Republic of China

    Qiaomin Xiang

  3. School of Sciences, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Xinxing Wu

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  1. Zongbin Yin
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  3. Xinxing Wu
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Correspondence to Zongbin Yin.

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Yin, Z., Xiang, Q. & Wu, X. Reiterative Distributional Chaos in Non-autonomous Discrete Systems. Qual. Theory Dyn. Syst. 20, 88 (2021). https://doi.org/10.1007/s12346-021-00526-1

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