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From iterated function systems to iterated multifunction systems

Author

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  • Herb E. KUNZE

    ()

  • Davide LA TORRE

    ()

  • Edward R. VRSCAY

    ()

Abstract

Starting from the original definitions of Iterated Function Systems (IFS) and Iterated Function Systems with Probabilities (IFSP) we introduce the notions of Iterated Multifunction Systems (IMS) and Iterated Multifunction Systems with Probabilities (IMSP). We consider the IMS and IMSP as operators on the space H(H(X)), the space of (nonempty) compact subsets of the space H(X) of (nonempty) compactsubsets of the complete metric "base space" or "pixel space" (X,d) onwhich the attractors are supported. A number of examples are provided.

Suggested Citation

  • Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2008-39
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    File URL: http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_039wp.pdf
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    References listed on IDEAS

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    1. Davide La Torre & Herb Kunze & Ed Vrscay, 2006. "Contractive multifunctions, fixed point inclusions and iterated multifunction systems," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1025, Universitá degli Studi di Milano.
    2. Davide LA TORRE & Franklin MENDIVIL, 2007. "Iterated function systems on multifunctions and inverse problems," Departmental Working Papers 2007-32, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
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    Cited by:

    1. Alberto BUCCI & Herb E. KUNZE & Davide LA TORRE, 2008. "Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model," Departmental Working Papers 2008-34, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Davide LA TORRE & Edward R. VRSCAY, 2008. "A generalized fractal transform for measure-valued images," Departmental Working Papers 2008-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Vincenzo CAPASSO & Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "Parameter identification for deterministic and stochastic differential equations using the "collage method" for fixed point equations," Departmental Working Papers 2008-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

    More about this item

    Keywords

    Multifunctions; self-similarity; generalized fractal transforms; iterated function system;

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