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Shift spaces and distributional chaos

Author

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  • Oprocha, Piotr
  • Wilczyński, Paweł

Abstract

We give sufficient conditions for a shift to be distributionally chaotic and chaotic in the sense of Li and Yorke. In the case of cocyclic shifts we show the equivalence between distributional chaos, chaos in the sense of Li and Yorke, positivity of entropy and uncountability of subshift.

Suggested Citation

  • Oprocha, Piotr & Wilczyński, Paweł, 2007. "Shift spaces and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 347-355.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:2:p:347-355
    DOI: 10.1016/j.chaos.2005.09.069
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    Cited by:

    1. Li, Risong & Wang, Hongqing & Zhao, Yu, 2016. "Kato’s chaos in duopoly games," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 69-72.
    2. 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.
    3. Yu Zhao & Risong Li, 2019. "Chaos in Duopoly Games via Furstenberg Family Couple," Complexity, Hindawi, vol. 2019, pages 1-8, November.
    4. 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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