Attractors of iterated function systems and Markov operators. (English) Zbl 1034.47002

Myjak, Józef; Szarek, Tomasz

Abstr. Appl. Anal. 2003, No. 8, 479-502 (2003).

The aim of the present paper is to give a review of results concerning “generalized” attractors for a large class of iterated function systems \(\{w_i\mid i\in I\}\) acting on a complete separable metric space which allows the consideration of a new class of sets with many interesting properties called semi-attractors or semifractals.
Furthermore, the authors present some fixed-point results for Markov operators acting on the space of Borel measures in order to develop some relations between semi-attractors and supports of invariant measures for the aforementioned Markov operators and between multifunctions and transition functions appearing in the theory of Markov operators.

Reviewer: Cryssoula Ganatsiou (Volos)

MSC:

47A35	Ergodic theory of linear operators
60J05	Discrete-time Markov processes on general state spaces
28D15	General groups of measure-preserving transformations
60J75	Jump processes (MSC2010)

Keywords:

iterated function systems; semi-attractors; semifractals; Markov operators; space of Borel measures