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On mixing property in set-valued discrete systems

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  • Gu, Rongbao
  • Guo, Wenjing

Abstract

Let (X,d) be a compact metric space and f:X→X be a continuous map. Let (K(X),H) be the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f¯:K(X)→K(X) be the map defined by f¯(A):{f(a):a∈A}. In this paper we investigate the relationships between the mixing property of (K(X),f¯) and the mixing property of (X,f). In addition, we discuss specification for the set-valued discrete dynamical system (K(X),f¯).

Suggested Citation

  • Gu, Rongbao & Guo, Wenjing, 2006. "On mixing property in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 747-754.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:3:p:747-754
    DOI: 10.1016/j.chaos.2005.04.004
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    References listed on IDEAS

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    1. Wu, Chen & Xu, Zhengjie & Lin, Wei & Ruan, Jiong, 2005. "Stochastic properties in Devaney’s chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1195-1199.
    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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    Cited by:

    1. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    2. Kwietniak, Dominik & Oprocha, Piotr, 2007. "Topological entropy and chaos for maps induced on hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 76-86.
    3. 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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