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On the Iteration Invariance of Distributional Chaos of Type \(2\frac{1}{2}\) in Non-autonomous Discrete System

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Abstract

This paper is concerned with invariants for distributional chaos of type \(2\frac{1}{2}\) in non-autonomous discrete system \((X, f_{1,\infty })\) which converges uniformly and proves that \(f_{1,\infty }\) is \(\text {DC}2\frac{1}{2}\) if and only if \(f_{1,\infty }^{[k]}\) is \(\text {DC}2\frac{1}{2}\) for any \(k\in \mathbb {N}\). This result partly answers the questions posed by Wu and Zhu (Appl Math Lett 26:432–436, 2013).

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Acknowledgements

Funding was provided by Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications (Grant No. 18TD0013) and National Natural Science Foundation of China (Grant No. 11601449) and Scientific Research Fund of the Sichuan Provincial Education Department (Grant No. 035Z2262).

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  1. School of Science, Sichuan Agricultural University, Yaan, 625014, Sichuan, People’s Republic of China

    Jianjun Wang

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  1. Jianjun Wang
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This project was supported by the National Natural Science Foundation of China (No. 11601449), the Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications (No. 18TD0013), and Scientific Research Fund of the Sichuan Provincial Education Department (No. 035Z2262).

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Wang, J. On the Iteration Invariance of Distributional Chaos of Type \(2\frac{1}{2}\) in Non-autonomous Discrete System. Qual. Theory Dyn. Syst. 18, 711–721 (2019). https://doi.org/10.1007/s12346-018-0308-x

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  • DOI: https://doi.org/10.1007/s12346-018-0308-x

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