## Abstract and Applied Analysis

### Attractors of iterated function systems and Markov operators

#### Abstract

This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems $\{w_{i}:i\in I\}$ 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.

#### Article information

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

Dates
First available in Project Euclid: 27 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1051453544

Digital Object Identifier
doi:10.1155/S1085337503212033

Mathematical Reviews number (MathSciNet)
MR1983076

Zentralblatt MATH identifier
1034.47002

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

#### Citation

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