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Devaney’s chaotic on induced maps of hyperspace

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  • Zhang, Gengrong
  • Zeng, Fanping
  • Liu, Xinhe

Abstract

Let (X,d) be a metric space and let f:X→X be a continuous map. In Section 2, the relationships among the chaoticity of f¯, f˜ and f are investigated while 2X, C(X) are taken We-topology. In Section 3, the relationships among the chaoticity of f¯, f˜, and f are investigated while X is a graph.

Suggested Citation

  • Zhang, Gengrong & Zeng, Fanping & Liu, Xinhe, 2006. "Devaney’s chaotic on induced maps of hyperspace," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 471-475.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:2:p:471-475
    DOI: 10.1016/j.chaos.2005.03.053
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    References listed on IDEAS

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    1. Fedeli, Alessandro, 2005. "On chaotic set-valued discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1381-1384.
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    Cited by:

    1. Kwietniak, Dominik & Oprocha, Piotr, 2007. "Topological entropy and chaos for maps induced on hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 76-86.
    2. Fu, Heman & Xing, Zhitao, 2012. "Mixing properties of set-valued maps on hyperspaces via Furstenberg families," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 439-443.

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