Attractors of iterated function systems and Markov operators

Józef Myjak and Tomasz Szarek

Abstract and Applied Analysis, 2003, vol. 2003, 1-24

Abstract:

This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems { w i : 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:373786

DOI: 10.1155/S1085337503212033

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