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21 April 2003 Attractors of iterated function systems and Markov operators
Józef Myjak, Tomasz Szarek
Abstr. Appl. Anal. 2003(8): 479-502 (21 April 2003). DOI: 10.1155/S1085337503212033


This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems {wi:iI} acting on a complete separable metric space. This generalization, which originates in the Banach contraction principle, allows us to consider a new class of sets, which we call semi-attractors (or semifractals). These sets have many interesting properties. Moreover, we give some fixed-point results for Markov operators acting on the space of Borel measures, and we show some relations between semi-attractors and supports of invariant measures for such Markov operators. Finally, we also show some relations between multifunctions and transition functions appearing in the theory of Markov operators.


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Józef Myjak. Tomasz Szarek. "Attractors of iterated function systems and Markov operators." Abstr. Appl. Anal. 2003 (8) 479 - 502, 21 April 2003.


Published: 21 April 2003
First available in Project Euclid: 27 April 2003

zbMATH: 1034.47002
MathSciNet: MR1983076
Digital Object Identifier: 10.1155/S1085337503212033

Primary: 47A35 , 60J05
Secondary: 28D15 , 60J75

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 8 • 21 April 2003
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