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Li‐Yorke Sensitivity of Set‐Valued Discrete Systems

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Listed:
  • Heng Liu
  • Fengchun Lei
  • Lidong Wang

Abstract

Consider the surjective, continuous map f : X → X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 𝒦(X) is the space of all nonempty compact subsets of X endowed with the Hausdorff metric. In this paper, we give a short proof that if f¯ is Li‐Yoke sensitive, then f is Li‐Yorke sensitive. Furthermore, we give an example showing that Li‐Yorke sensitivity of f does not imply Li‐Yorke sensitivity of f¯.

Suggested Citation

  • Heng Liu & Fengchun Lei & Lidong Wang, 2013. "Li‐Yorke Sensitivity of Set‐Valued Discrete Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:260856
    DOI: 10.1155/2013/260856
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    References listed on IDEAS

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    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. Banks, John, 2005. "Chaos for induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 681-685.
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