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1995/1996 Chaotic maps in hyperspace
Hermann Haase
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Real Anal. Exchange 21(2): 689-695 (1995/1996).


The dynamical system \((\mathcal{F}(X),T)\) which arises from an iterated function system \((X;w_1,\ldots ,w_m)\), where \(X\) is a compact metric space identified with the attractor of the system and the \(w_i\)’s are contractive invertible maps, is chaotic provided that the iterated function system satisfies the open set condition. The map \(T\) on the hyperspace \(\mathcal{F} (X)\) of the closed subsets of \(X\) is defined for a closed subset \(E\) as \begin{equation*} T(E)=w_1^{-1}(E)\cup \ldots \cup w_m^{-1}(E). \end{equation*} This extends results about the shift dynamical system for the non-overlapping case \cite{ba}.


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Hermann Haase. "Chaotic maps in hyperspace." Real Anal. Exchange 21 (2) 689 - 695, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 14 June 2012

zbMATH: 0879.54044
MathSciNet: MR1407280

Primary: 54B20 , 54H20‎
Secondary: ‎54C60‎

Keywords: hyperspace , IFS , set-valued chaotic map

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 2 • 1995/1996
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