Abstract and Applied Analysis

Attractors of iterated function systems and Markov operators

Józef Myjak and Tomasz Szarek

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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.

Article information

Abstr. Appl. Anal., Volume 2003, Number 8 (2003), 479-502.

First available in Project Euclid: 27 April 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx] 60J05
Secondary: 28D15 60J75


Myjak, Józef; Szarek, Tomasz. Attractors of iterated function systems and Markov operators. Abstr. Appl. Anal. 2003 (2003), no. 8, 479--502. doi:10.1155/S1085337503212033. https://projecteuclid.org/euclid.aaa/1051453544

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