Abstract and Applied Analysis

Attractors of iterated function systems and Markov operators

Józef Myjak and Tomasz Szarek

Full-text: Open access

Abstract

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

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


Export citation