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Sensitivity for set-valued maps induced by M-systems

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  • Hou, Bingzhe
  • Liao, Gongfu
  • Liu, Heng

Abstract

Consider a continuous map f:X→X and the continuous map f¯ of K(X) into itself induced by f, where X is a compact metric space without isolated points and K(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper, we discuss the sensitivity of the set valued maps induced by M-systems. In fact, we prove that if (X,f) is a non-minimal M-system, then f¯ is sensitive; and give an example to show the possibility that f¯ is sensitive when (X,f) is a, minimal but not weakly mixing, M-system.

Suggested Citation

  • Hou, Bingzhe & Liao, Gongfu & Liu, Heng, 2008. "Sensitivity for set-valued maps induced by M-systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1075-1080.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1075-1080
    DOI: 10.1016/j.chaos.2007.02.015
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    References listed on IDEAS

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    1. Peris, Alfredo, 2005. "Set-valued discrete chaos," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 19-23.
    2. Fedeli, Alessandro, 2005. "On chaotic set-valued discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1381-1384.
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    4. Banks, John, 2005. "Chaos for induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 681-685.
    5. Kwietniak, Dominik & Oprocha, Piotr, 2007. "Topological entropy and chaos for maps induced on hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 76-86.
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