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The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets

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  • Risong Li
  • Tianxiu Lu

Abstract

In this paper, we study some chaotic properties of - dimensional dynamical system of the form where for any is an integer, and is a compact subinterval of the real line for any . Particularly, a necessary and sufficient condition for a cyclic permutation map to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropy of such a cyclic permutation map is the same as the topological entropy of each of the following maps: if and , and that is sensitive if and only if at least one of the coordinates maps of is sensitive.

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  • Risong Li & Tianxiu Lu, 2020. "The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets," Complexity, Hindawi, vol. 2020, pages 1-12, September.
    • Handle: RePEc:hin:complx:9379628
    DOI: 10.1155/2020/9379628
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    Cited by:

    1. Hongqing Wang & Tianxiu Lu & Risong Li & Yuanlin Chen & Yongjiang Li & Weizhen Quan, 2022. "Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    2. Yu Zhao & Waseem Anwar & Risong Li & Tianxiu Lu & Zhiwen Mo, 2023. "Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps," Mathematics, MDPI, vol. 11(15), pages 1-9, July.

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