Attractors of iterated function systems and Markov operators

Józef Myjak and Tomasz Szarek

Abstract and Applied Analysis, 2003, vol. 2003, issue 8, 479-502

Abstract: This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems {wi : i ∈ I} 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.

Date: 2003
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https://doi.org/10.1155/S1085337503212033

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:8:p:479-502

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