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Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps

Author

Listed:
  • Risong Li
  • Tianxiu Lu
  • Jingmin Pi
  • Waseem Anwar

Abstract

Let hss=1∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W. In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3)).

Suggested Citation

  • Risong Li & Tianxiu Lu & Jingmin Pi & Waseem Anwar, 2022. "Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:5481666
    DOI: 10.1155/2022/5481666
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    References listed on IDEAS

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    1. Balibrea, F. & Smı́tal, J. & Štefánková, M., 2005. "The three versions of distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1581-1583.
    2. Yan, Kesong & Zeng, Fanping & Zhang, Gengrong, 2011. "Devaney’s chaos on uniform limit maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 522-525.
    3. Li, Risong, 2012. "A note on uniform convergence and transitivity," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 759-764.
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