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). The notion of IMS has been introduced by the same authors in a previous paper and this work represents an extension of it. 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) compact subsets of the complete metric "base space" or "pixel space" (X,d) on which the attractors are supported. A number of examples are provided
From iterated function systems to iterated multifunction systems / H. Kunze, D. La Torre, E.R. Vrscay. - In: COMMUNICATIONS ON APPLIED NONLINEAR ANALYSIS. - ISSN 1074-133X. - 15:4(2008 Oct), pp. 1-13.
From iterated function systems to iterated multifunction systems
D. La TorreSecondo
;
2008
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). The notion of IMS has been introduced by the same authors in a previous paper and this work represents an extension of it. 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) compact subsets of the complete metric "base space" or "pixel space" (X,d) on which the attractors are supported. A number of examples are provided
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